Catalan.tbl.md

Catalan

['A128899', 'A039598']

Catalan Triangle view

Row	Seq
Row0	[1]
Row1	[0, 1]
Row2	[0, 2, 1]
Row3	[0, 5, 4, 1]
Row4	[0, 14, 14, 6, 1]
Row5	[0, 42, 48, 27, 8, 1]
Row6	[0, 132, 165, 110, 44, 10, 1]
Row7	[0, 429, 572, 429, 208, 65, 12, 1]
Row8	[0, 1430, 2002, 1638, 910, 350, 90, 14, 1]
Row9	[0, 4862, 7072, 6188, 3808, 1700, 544, 119, 16, 1]

Catalan Triangles

Flat	Seq
Triangle	[[1], [0, 1], [0, 2, 1], [0, 5, 4, 1], [0, 14, 14, 6, 1], [0, 42, 48, 27, 8, 1], [0, 132, 165, 110, 44, 10, 1], [0, 429, 572, 429, 208, 65, 12, 1], [0, 1430, 2002, 1638, 910, 350, 90, 14, 1], [0, 4862, 7072, 6188, 3808, 1700, 544, 119, 16, 1]]
RevTabl	[[1], [1, 0], [1, 2, 0], [1, 4, 5, 0], [1, 6, 14, 14, 0], [1, 8, 27, 48, 42, 0], [1, 10, 44, 110, 165, 132, 0], [1, 12, 65, 208, 429, 572, 429, 0], [1, 14, 90, 350, 910, 1638, 2002, 1430, 0], [1, 16, 119, 544, 1700, 3808, 6188, 7072, 4862, 0]]
AntiDiag	[[1], [0], [0, 1], [0, 2], [0, 5, 1], [0, 14, 4], [0, 42, 14, 1], [0, 132, 48, 6], [0, 429, 165, 27, 1], [0, 1430, 572, 110, 8]]
AccTabl	[[1], [0, 1], [0, 2, 3], [0, 5, 9, 10], [0, 14, 28, 34, 35], [0, 42, 90, 117, 125, 126], [0, 132, 297, 407, 451, 461, 462], [0, 429, 1001, 1430, 1638, 1703, 1715, 1716], [0, 1430, 3432, 5070, 5980, 6330, 6420, 6434, 6435], [0, 4862, 11934, 18122, 21930, 23630, 24174, 24293, 24309, 24310]]
RevAccTabl	[[1], [1, 0], [3, 2, 0], [10, 9, 5, 0], [35, 34, 28, 14, 0], [126, 125, 117, 90, 42, 0], [462, 461, 451, 407, 297, 132, 0], [1716, 1715, 1703, 1638, 1430, 1001, 429, 0], [6435, 6434, 6420, 6330, 5980, 5070, 3432, 1430, 0], [24310, 24309, 24293, 24174, 23630, 21930, 18122, 11934, 4862, 0]]
AccRevTabl	[[1], [1, 1], [1, 3, 3], [1, 5, 10, 10], [1, 7, 21, 35, 35], [1, 9, 36, 84, 126, 126], [1, 11, 55, 165, 330, 462, 462], [1, 13, 78, 286, 715, 1287, 1716, 1716], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310]]
DiffxTabl	[[1], [0, 2], [0, 4, 3], [0, 10, 12, 4], [0, 28, 42, 24, 5], [0, 84, 144, 108, 40, 6], [0, 264, 495, 440, 220, 60, 7], [0, 858, 1716, 1716, 1040, 390, 84, 8], [0, 2860, 6006, 6552, 4550, 2100, 630, 112, 9], [0, 9724, 21216, 24752, 19040, 10200, 3808, 952, 144, 10]]

Catalan Row sums

Trait	Seq
RowSum	[1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310]
EvenSum	[1, 0, 1, 4, 15, 56, 210, 792, 3003, 11440]
OddSum	[0, 1, 2, 6, 20, 70, 252, 924, 3432, 12870]
AltSum	[1, -1, -1, -2, -5, -14, -42, -132, -429, -1430]
AbsSum	[1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310]
AccSum	[1, 1, 5, 24, 111, 500, 2210, 9632, 41531, 177564]
AccRevSum	[1, 2, 7, 26, 99, 382, 1486, 5812, 22819, 89846]
DiagSum	[1, 0, 1, 2, 6, 18, 57, 186, 622, 2120]

Catalan Transforms

Trans	Seq
RowLcm	[1, 1, 2, 20, 42, 3024, 660, 34320, 450450, 13613600]
RowGcd	[1, 1, 2, 1, 2, 1, 1, 1, 2, 1]
RowMax	[1, 1, 2, 5, 14, 48, 165, 572, 2002, 7072]
CentralE	[1, 2, 14, 110, 910]
CentralO	[0, 5, 48, 429, 3808]
ColMiddle	[1, 0, 2, 5, 14, 48, 110, 429, 910, 3808]
ColLeft	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv	[1, 1, 5, 28, 165, 1001, 6188, 38760, 245157, 1562275]
InvBinConv	[1, 1, -3, 4, 5, -39, 84, 8, -603, 1795]
TransSqrs	[0, 1, 6, 30, 140, 630, 2772, 12012, 51480, 218790]
TransNat0	[0, 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536]
TransNat1	[1, 2, 7, 26, 99, 382, 1486, 5812, 22819, 89846]
PosHalf	[1, 1, 5, 29, 181, 1181, 7941, 54573, 381333, 2699837]
NegHalf	[1, 1, -3, 13, -67, 381, -2307, 14589, -95235, 636925]

Catalan Diagonals as rows

DiagRow	Seq
DiagRow0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1	[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]
DiagRow2	[0, 5, 14, 27, 44, 65, 90, 119, 152, 189]
DiagRow3	[0, 14, 48, 110, 208, 350, 544, 798, 1120, 1518]
DiagRow4	[0, 42, 165, 429, 910, 1700, 2907, 4655, 7084, 10350]
DiagRow5	[0, 132, 572, 1638, 3808, 7752, 14364, 24794, 40480, 63180]
DiagRow6	[0, 429, 2002, 6188, 15504, 33915, 67298, 123970, 215280, 356265]
DiagRow7	[0, 1430, 7072, 23256, 62016, 144210, 303600, 592020, 1085760, 1893294]
DiagRow8	[0, 4862, 25194, 87210, 245157, 600875, 1332045, 2731365, 5259150, 9612108]
DiagRow9	[0, 16796, 90440, 326876, 961400, 2466750, 5722860, 12271350, 24682944, 47071640]

Catalan Diagonals as columns

DiagCol	Seq
DiagCol0	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1	[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796]
DiagCol2	[1, 4, 14, 48, 165, 572, 2002, 7072, 25194, 90440]
DiagCol3	[1, 6, 27, 110, 429, 1638, 6188, 23256, 87210, 326876]
DiagCol4	[1, 8, 44, 208, 910, 3808, 15504, 62016, 245157, 961400]
DiagCol5	[1, 10, 65, 350, 1700, 7752, 33915, 144210, 600875, 2466750]
DiagCol6	[1, 12, 90, 544, 2907, 14364, 67298, 303600, 1332045, 5722860]
DiagCol7	[1, 14, 119, 798, 4655, 24794, 123970, 592020, 2731365, 12271350]
DiagCol8	[1, 16, 152, 1120, 7084, 40480, 215280, 1085760, 5259150, 24682944]
DiagCol9	[1, 18, 189, 1518, 10350, 63180, 356265, 1893294, 9612108, 47071640]

Catalan Polynomial values as rows

PolyRow	Seq
PolyRow0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1	[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2	[0, 3, 8, 15, 24, 35, 48, 63, 80, 99]
PolyRow3	[0, 10, 34, 78, 148, 250, 390, 574, 808, 1098]
PolyRow4	[0, 35, 148, 411, 920, 1795, 3180, 5243, 8176, 12195]
PolyRow5	[0, 126, 652, 2178, 5736, 12910, 25956, 47922, 82768, 135486]
PolyRow6	[0, 462, 2892, 11574, 35808, 92910, 211932, 438102, 837984, 1505358]
PolyRow7	[0, 1716, 12882, 61596, 223668, 668820, 1730646, 4005372, 8484456, 16726068]
PolyRow8	[0, 6435, 57540, 328083, 1397496, 4815075, 14133180, 36620115, 85904688, 185844771]
PolyRow9	[0, 24310, 257500, 1748346, 8732920, 34667110, 115419540, 334811050, 869783536, 2064940470]

Catalan Polynomial values as columns

PolyCol	Seq
PolyCol0	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1	[1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310]
PolyCol2	[1, 2, 8, 34, 148, 652, 2892, 12882, 57540, 257500]
PolyCol3	[1, 3, 15, 78, 411, 2178, 11574, 61596, 328083, 1748346]
PolyCol4	[1, 4, 24, 148, 920, 5736, 35808, 223668, 1397496, 8732920]
PolyCol5	[1, 5, 35, 250, 1795, 12910, 92910, 668820, 4815075, 34667110]
PolyCol6	[1, 6, 48, 390, 3180, 25956, 211932, 1730646, 14133180, 115419540]
PolyCol7	[1, 7, 63, 574, 5243, 47922, 438102, 4005372, 36620115, 334811050]
PolyCol8	[1, 8, 80, 808, 8176, 82768, 837984, 8484456, 85904688, 869783536]
PolyCol9	[1, 9, 99, 1098, 12195, 135486, 1505358, 16726068, 185844771, 2064940470]

Catalan:Inv

[]

Catalan:Inv Triangle view

Row	Seq
Row0	[1]
Row1	[0, 1]
Row2	[0, -2, 1]
Row3	[0, 3, -4, 1]
Row4	[0, -4, 10, -6, 1]
Row5	[0, 5, -20, 21, -8, 1]
Row6	[0, -6, 35, -56, 36, -10, 1]
Row7	[0, 7, -56, 126, -120, 55, -12, 1]
Row8	[0, -8, 84, -252, 330, -220, 78, -14, 1]
Row9	[0, 9, -120, 462, -792, 715, -364, 105, -16, 1]

Catalan:Inv Triangles

Flat	Seq
Triangle	[[1], [0, 1], [0, -2, 1], [0, 3, -4, 1], [0, -4, 10, -6, 1], [0, 5, -20, 21, -8, 1], [0, -6, 35, -56, 36, -10, 1], [0, 7, -56, 126, -120, 55, -12, 1], [0, -8, 84, -252, 330, -220, 78, -14, 1], [0, 9, -120, 462, -792, 715, -364, 105, -16, 1]]
RevTabl	[[1], [1, 0], [1, -2, 0], [1, -4, 3, 0], [1, -6, 10, -4, 0], [1, -8, 21, -20, 5, 0], [1, -10, 36, -56, 35, -6, 0], [1, -12, 55, -120, 126, -56, 7, 0], [1, -14, 78, -220, 330, -252, 84, -8, 0], [1, -16, 105, -364, 715, -792, 462, -120, 9, 0]]
AntiDiag	[[1], [0], [0, 1], [0, -2], [0, 3, 1], [0, -4, -4], [0, 5, 10, 1], [0, -6, -20, -6], [0, 7, 35, 21, 1], [0, -8, -56, -56, -8]]
AccTabl	[[1], [0, 1], [0, -2, -1], [0, 3, -1, 0], [0, -4, 6, 0, 1], [0, 5, -15, 6, -2, -1], [0, -6, 29, -27, 9, -1, 0], [0, 7, -49, 77, -43, 12, 0, 1], [0, -8, 76, -176, 154, -66, 12, -2, -1], [0, 9, -111, 351, -441, 274, -90, 15, -1, 0]]
RevAccTabl	[[1], [1, 0], [-1, -2, 0], [0, -1, 3, 0], [1, 0, 6, -4, 0], [-1, -2, 6, -15, 5, 0], [0, -1, 9, -27, 29, -6, 0], [1, 0, 12, -43, 77, -49, 7, 0], [-1, -2, 12, -66, 154, -176, 76, -8, 0], [0, -1, 15, -90, 274, -441, 351, -111, 9, 0]]
AccRevTabl	[[1], [1, 1], [1, -1, -1], [1, -3, 0, 0], [1, -5, 5, 1, 1], [1, -7, 14, -6, -1, -1], [1, -9, 27, -29, 6, 0, 0], [1, -11, 44, -76, 50, -6, 1, 1], [1, -13, 65, -155, 175, -77, 7, -1, -1], [1, -15, 90, -274, 441, -351, 111, -9, 0, 0]]
DiffxTabl	[[1], [0, 2], [0, -4, 3], [0, 6, -12, 4], [0, -8, 30, -24, 5], [0, 10, -60, 84, -40, 6], [0, -12, 105, -224, 180, -60, 7], [0, 14, -168, 504, -600, 330, -84, 8], [0, -16, 252, -1008, 1650, -1320, 546, -112, 9], [0, 18, -360, 1848, -3960, 4290, -2548, 840, -144, 10]]

Catalan:Inv Row sums

Trait	Seq
RowSum	[1, 1, -1, 0, 1, -1, 0, 1, -1, 0]
EvenSum	[1, 0, 1, -4, 11, -28, 72, -188, 493, -1292]
OddSum	[0, 1, -2, 4, -10, 27, -72, 189, -494, 1292]
AltSum	[1, -1, 3, -8, 21, -55, 144, -377, 987, -2584]
AbsSum	[1, 1, 3, 8, 21, 55, 144, 377, 987, 2584]
AccSum	[1, 1, -3, 2, 3, -7, 4, 5, -11, 6]
AccRevSum	[1, 2, -1, -2, 3, 0, -4, 4, 1, -6]
DiagSum	[1, 0, 1, -2, 4, -8, 16, -32, 64, -128]

Catalan:Inv Transforms

Trans	Seq
RowLcm	[1, 1, 2, 12, 60, 840, 2520, 27720, 360360, 720720]
RowGcd	[1, 1, 2, 1, 2, 1, 1, 1, 2, 1]
RowMax	[1, 1, 2, 4, 10, 21, 56, 126, 330, 792]
CentralE	[1, -2, 10, -56, 330]
CentralO	[0, 3, -20, 126, -792]
ColMiddle	[1, 0, -2, 3, 10, -20, -56, 126, 330, -792]
ColLeft	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
BinConv	[1, 1, -3, -2, 21, -4, -150, 155, 1029, -2072]
InvBinConv	[1, 1, 5, 22, 101, 476, 2282, 11075, 54245, 267592]
TransSqrs	[0, 1, 2, -4, -2, 11, -8, -11, 26, -12]
TransNat0	[0, 1, 0, -2, 2, 1, -4, 3, 2, -6]
TransNat1	[1, 2, -1, -2, 3, 0, -4, 4, 1, -6]
PosHalf	[1, 1, -3, 5, -3, -11, 45, -91, 93, 85]
NegHalf	[1, 1, 5, 21, 85, 341, 1365, 5461, 21845, 87381]

Catalan:Inv Diagonals as rows

DiagRow	Seq
DiagRow0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow1	[0, -2, -4, -6, -8, -10, -12, -14, -16, -18]
DiagRow2	[0, 3, 10, 21, 36, 55, 78, 105, 136, 171]
DiagRow3	[0, -4, -20, -56, -120, -220, -364, -560, -816, -1140]
DiagRow4	[0, 5, 35, 126, 330, 715, 1365, 2380, 3876, 5985]
DiagRow5	[0, -6, -56, -252, -792, -2002, -4368, -8568, -15504, -26334]
DiagRow6	[0, 7, 84, 462, 1716, 5005, 12376, 27132, 54264, 100947]
DiagRow7	[0, -8, -120, -792, -3432, -11440, -31824, -77520, -170544, -346104]
DiagRow8	[0, 9, 165, 1287, 6435, 24310, 75582, 203490, 490314, 1081575]
DiagRow9	[0, -10, -220, -2002, -11440, -48620, -167960, -497420, -1307504, -3124550]

Catalan:Inv Diagonals as columns

DiagCol	Seq
DiagCol0	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1	[1, -2, 3, -4, 5, -6, 7, -8, 9, -10]
DiagCol2	[1, -4, 10, -20, 35, -56, 84, -120, 165, -220]
DiagCol3	[1, -6, 21, -56, 126, -252, 462, -792, 1287, -2002]
DiagCol4	[1, -8, 36, -120, 330, -792, 1716, -3432, 6435, -11440]
DiagCol5	[1, -10, 55, -220, 715, -2002, 5005, -11440, 24310, -48620]
DiagCol6	[1, -12, 78, -364, 1365, -4368, 12376, -31824, 75582, -167960]
DiagCol7	[1, -14, 105, -560, 2380, -8568, 27132, -77520, 203490, -497420]
DiagCol8	[1, -16, 136, -816, 3876, -15504, 54264, -170544, 490314, -1307504]
DiagCol9	[1, -18, 171, -1140, 5985, -26334, 100947, -346104, 1081575, -3124550]

Catalan:Inv Polynomial values as rows

PolyRow	Seq
PolyRow0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1	[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2	[0, -1, 0, 3, 8, 15, 24, 35, 48, 63]
PolyRow3	[0, 0, -2, 0, 12, 40, 90, 168, 280, 432]
PolyRow4	[0, 1, 0, -3, 16, 105, 336, 805, 1632, 2961]
PolyRow5	[0, -1, 2, -3, 20, 275, 1254, 3857, 9512, 20295]
PolyRow6	[0, 0, 0, 0, 24, 720, 4680, 18480, 55440, 139104]
PolyRow7	[0, 1, -2, 3, 28, 1885, 17466, 88543, 323128, 953433]
PolyRow8	[0, -1, 0, 3, 32, 4935, 65184, 424235, 1883328, 6534927]
PolyRow9	[0, 0, 2, 0, 36, 12920, 243270, 2032632, 10976840, 44791056]

Catalan:Inv Polynomial values as columns

PolyCol	Seq
PolyCol0	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1	[1, 1, -1, 0, 1, -1, 0, 1, -1, 0]
PolyCol2	[1, 2, 0, -2, 0, 2, 0, -2, 0, 2]
PolyCol3	[1, 3, 3, 0, -3, -3, 0, 3, 3, 0]
PolyCol4	[1, 4, 8, 12, 16, 20, 24, 28, 32, 36]
PolyCol5	[1, 5, 15, 40, 105, 275, 720, 1885, 4935, 12920]
PolyCol6	[1, 6, 24, 90, 336, 1254, 4680, 17466, 65184, 243270]
PolyCol7	[1, 7, 35, 168, 805, 3857, 18480, 88543, 424235, 2032632]
PolyCol8	[1, 8, 48, 280, 1632, 9512, 55440, 323128, 1883328, 10976840]
PolyCol9	[1, 9, 63, 432, 2961, 20295, 139104, 953433, 6534927, 44791056]

Catalan:Rev

[]

Catalan:Rev Triangle view

Row	Seq
Row0	[1]
Row1	[1, 0]
Row2	[1, 2, 0]
Row3	[1, 4, 5, 0]
Row4	[1, 6, 14, 14, 0]
Row5	[1, 8, 27, 48, 42, 0]
Row6	[1, 10, 44, 110, 165, 132, 0]
Row7	[1, 12, 65, 208, 429, 572, 429, 0]
Row8	[1, 14, 90, 350, 910, 1638, 2002, 1430, 0]
Row9	[1, 16, 119, 544, 1700, 3808, 6188, 7072, 4862, 0]

Catalan:Rev Triangles

Flat	Seq
Triangle	[[1], [1, 0], [1, 2, 0], [1, 4, 5, 0], [1, 6, 14, 14, 0], [1, 8, 27, 48, 42, 0], [1, 10, 44, 110, 165, 132, 0], [1, 12, 65, 208, 429, 572, 429, 0], [1, 14, 90, 350, 910, 1638, 2002, 1430, 0], [1, 16, 119, 544, 1700, 3808, 6188, 7072, 4862, 0]]
RevTabl	[[1], [0, 1], [0, 2, 1], [0, 5, 4, 1], [0, 14, 14, 6, 1], [0, 42, 48, 27, 8, 1], [0, 132, 165, 110, 44, 10, 1], [0, 429, 572, 429, 208, 65, 12, 1], [0, 1430, 2002, 1638, 910, 350, 90, 14, 1], [0, 4862, 7072, 6188, 3808, 1700, 544, 119, 16, 1]]
AntiDiag	[[1], [1], [1, 0], [1, 2], [1, 4, 0], [1, 6, 5], [1, 8, 14, 0], [1, 10, 27, 14], [1, 12, 44, 48, 0], [1, 14, 65, 110, 42]]
AccTabl	[[1], [1, 1], [1, 3, 3], [1, 5, 10, 10], [1, 7, 21, 35, 35], [1, 9, 36, 84, 126, 126], [1, 11, 55, 165, 330, 462, 462], [1, 13, 78, 286, 715, 1287, 1716, 1716], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310]]
RevAccTabl	[[1], [1, 1], [3, 3, 1], [10, 10, 5, 1], [35, 35, 21, 7, 1], [126, 126, 84, 36, 9, 1], [462, 462, 330, 165, 55, 11, 1], [1716, 1716, 1287, 715, 286, 78, 13, 1], [6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1]]
AccRevTabl	[[1], [0, 1], [0, 2, 3], [0, 5, 9, 10], [0, 14, 28, 34, 35], [0, 42, 90, 117, 125, 126], [0, 132, 297, 407, 451, 461, 462], [0, 429, 1001, 1430, 1638, 1703, 1715, 1716], [0, 1430, 3432, 5070, 5980, 6330, 6420, 6434, 6435], [0, 4862, 11934, 18122, 21930, 23630, 24174, 24293, 24309, 24310]]
DiffxTabl	[[1], [1, 0], [1, 4, 0], [1, 8, 15, 0], [1, 12, 42, 56, 0], [1, 16, 81, 192, 210, 0], [1, 20, 132, 440, 825, 792, 0], [1, 24, 195, 832, 2145, 3432, 3003, 0], [1, 28, 270, 1400, 4550, 9828, 14014, 11440, 0], [1, 32, 357, 2176, 8500, 22848, 43316, 56576, 43758, 0]]

Catalan:Rev Row sums

Trait	Seq
RowSum	[1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310]
EvenSum	[1, 1, 1, 6, 15, 70, 210, 924, 3003, 12870]
OddSum	[0, 0, 2, 4, 20, 56, 252, 792, 3432, 11440]
AltSum	[1, 1, -1, 2, -5, 14, -42, 132, -429, 1430]
AbsSum	[1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310]
AccSum	[1, 2, 7, 26, 99, 382, 1486, 5812, 22819, 89846]
AccRevSum	[1, 1, 5, 24, 111, 500, 2210, 9632, 41531, 177564]
DiagSum	[1, 1, 1, 3, 5, 12, 23, 52, 105, 232]

Catalan:Rev Transforms

Trans	Seq
RowLcm	[1, 1, 2, 20, 42, 3024, 660, 34320, 450450, 13613600]
RowGcd	[1, 1, 2, 1, 2, 1, 1, 1, 2, 1]
RowMax	[1, 1, 2, 5, 14, 48, 165, 572, 2002, 7072]
CentralE	[1, 2, 14, 110, 910]
CentralO	[1, 4, 27, 208, 1700]
ColMiddle	[1, 1, 2, 4, 14, 27, 110, 208, 910, 1700]
ColLeft	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv	[1, 1, 5, 28, 165, 1001, 6188, 38760, 245157, 1562275]
InvBinConv	[1, -1, -3, -4, 5, 39, 84, -8, -603, -1795]
TransSqrs	[0, 0, 2, 24, 188, 1220, 7116, 38752, 201176, 1008252]
TransNat0	[0, 0, 2, 14, 76, 374, 1748, 7916, 35096, 153254]
TransNat1	[1, 1, 5, 24, 111, 500, 2210, 9632, 41531, 177564]
PosHalf	[1, 2, 8, 34, 148, 652, 2892, 12882, 57540, 257500]
NegHalf	[1, -2, 0, -2, -4, -12, -36, -114, -372, -1244]

Catalan:Rev Diagonals as rows

DiagRow	Seq
DiagRow0	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1	[1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796]
DiagRow2	[1, 4, 14, 48, 165, 572, 2002, 7072, 25194, 90440]
DiagRow3	[1, 6, 27, 110, 429, 1638, 6188, 23256, 87210, 326876]
DiagRow4	[1, 8, 44, 208, 910, 3808, 15504, 62016, 245157, 961400]
DiagRow5	[1, 10, 65, 350, 1700, 7752, 33915, 144210, 600875, 2466750]
DiagRow6	[1, 12, 90, 544, 2907, 14364, 67298, 303600, 1332045, 5722860]
DiagRow7	[1, 14, 119, 798, 4655, 24794, 123970, 592020, 2731365, 12271350]
DiagRow8	[1, 16, 152, 1120, 7084, 40480, 215280, 1085760, 5259150, 24682944]
DiagRow9	[1, 18, 189, 1518, 10350, 63180, 356265, 1893294, 9612108, 47071640]

Catalan:Rev Diagonals as columns

DiagCol	Seq
DiagCol0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1	[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]
DiagCol2	[0, 5, 14, 27, 44, 65, 90, 119, 152, 189]
DiagCol3	[0, 14, 48, 110, 208, 350, 544, 798, 1120, 1518]
DiagCol4	[0, 42, 165, 429, 910, 1700, 2907, 4655, 7084, 10350]
DiagCol5	[0, 132, 572, 1638, 3808, 7752, 14364, 24794, 40480, 63180]
DiagCol6	[0, 429, 2002, 6188, 15504, 33915, 67298, 123970, 215280, 356265]
DiagCol7	[0, 1430, 7072, 23256, 62016, 144210, 303600, 592020, 1085760, 1893294]
DiagCol8	[0, 4862, 25194, 87210, 245157, 600875, 1332045, 2731365, 5259150, 9612108]
DiagCol9	[0, 16796, 90440, 326876, 961400, 2466750, 5722860, 12271350, 24682944, 47071640]

Catalan:Rev Polynomial values as rows

PolyRow	Seq
PolyRow0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2	[1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
PolyRow3	[1, 10, 29, 58, 97, 146, 205, 274, 353, 442]
PolyRow4	[1, 35, 181, 523, 1145, 2131, 3565, 5531, 8113, 11395]
PolyRow5	[1, 126, 1181, 4966, 14289, 32966, 65821, 118686, 198401, 312814]
PolyRow6	[1, 462, 7941, 48838, 185193, 530526, 1265677, 2654646, 5060433, 8960878]
PolyRow7	[1, 1716, 54573, 492724, 2467137, 8786436, 25066621, 61189668, 133071009, 264735892]
PolyRow8	[1, 6435, 381333, 5068915, 33563481, 148733571, 507709165, 1443039123, 3581326065, 8006545891]
PolyRow9	[1, 24310, 2699837, 52955950, 464221105, 2561439806, 10466643805, 34648845862, 98156060225, 246643289830]

Catalan:Rev Polynomial values as columns

PolyCol	Seq
PolyCol0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1	[1, 1, 3, 10, 35, 126, 462, 1716, 6435, 24310]
PolyCol2	[1, 1, 5, 29, 181, 1181, 7941, 54573, 381333, 2699837]
PolyCol3	[1, 1, 7, 58, 523, 4966, 48838, 492724, 5068915, 52955950]
PolyCol4	[1, 1, 9, 97, 1145, 14289, 185193, 2467137, 33563481, 464221105]
PolyCol5	[1, 1, 11, 146, 2131, 32966, 530526, 8786436, 148733571, 2561439806]
PolyCol6	[1, 1, 13, 205, 3565, 65821, 1265677, 25066621, 507709165, 10466643805]
PolyCol7	[1, 1, 15, 274, 5531, 118686, 2654646, 61189668, 1443039123, 34648845862]
PolyCol8	[1, 1, 17, 353, 8113, 198401, 5060433, 133071009, 3581326065, 98156060225]
PolyCol9	[1, 1, 19, 442, 11395, 312814, 8960878, 264735892, 8006545891, 246643289830]

Catalan:Inv:Rev

[]

Catalan:Inv:Rev Triangle view

Row	Seq
Row0	[1]
Row1	[1, 0]
Row2	[1, -2, 0]
Row3	[1, -4, 3, 0]
Row4	[1, -6, 10, -4, 0]
Row5	[1, -8, 21, -20, 5, 0]
Row6	[1, -10, 36, -56, 35, -6, 0]
Row7	[1, -12, 55, -120, 126, -56, 7, 0]
Row8	[1, -14, 78, -220, 330, -252, 84, -8, 0]
Row9	[1, -16, 105, -364, 715, -792, 462, -120, 9, 0]

Catalan:Inv:Rev Triangles

Flat	Seq
Triangle	[[1], [1, 0], [1, -2, 0], [1, -4, 3, 0], [1, -6, 10, -4, 0], [1, -8, 21, -20, 5, 0], [1, -10, 36, -56, 35, -6, 0], [1, -12, 55, -120, 126, -56, 7, 0], [1, -14, 78, -220, 330, -252, 84, -8, 0], [1, -16, 105, -364, 715, -792, 462, -120, 9, 0]]
RevTabl	[[1], [0, 1], [0, -2, 1], [0, 3, -4, 1], [0, -4, 10, -6, 1], [0, 5, -20, 21, -8, 1], [0, -6, 35, -56, 36, -10, 1], [0, 7, -56, 126, -120, 55, -12, 1], [0, -8, 84, -252, 330, -220, 78, -14, 1], [0, 9, -120, 462, -792, 715, -364, 105, -16, 1]]
AntiDiag	[[1], [1], [1, 0], [1, -2], [1, -4, 0], [1, -6, 3], [1, -8, 10, 0], [1, -10, 21, -4], [1, -12, 36, -20, 0], [1, -14, 55, -56, 5]]
AccTabl	[[1], [1, 1], [1, -1, -1], [1, -3, 0, 0], [1, -5, 5, 1, 1], [1, -7, 14, -6, -1, -1], [1, -9, 27, -29, 6, 0, 0], [1, -11, 44, -76, 50, -6, 1, 1], [1, -13, 65, -155, 175, -77, 7, -1, -1], [1, -15, 90, -274, 441, -351, 111, -9, 0, 0]]
RevAccTabl	[[1], [1, 1], [-1, -1, 1], [0, 0, -3, 1], [1, 1, 5, -5, 1], [-1, -1, -6, 14, -7, 1], [0, 0, 6, -29, 27, -9, 1], [1, 1, -6, 50, -76, 44, -11, 1], [-1, -1, 7, -77, 175, -155, 65, -13, 1], [0, 0, -9, 111, -351, 441, -274, 90, -15, 1]]
AccRevTabl	[[1], [0, 1], [0, -2, -1], [0, 3, -1, 0], [0, -4, 6, 0, 1], [0, 5, -15, 6, -2, -1], [0, -6, 29, -27, 9, -1, 0], [0, 7, -49, 77, -43, 12, 0, 1], [0, -8, 76, -176, 154, -66, 12, -2, -1], [0, 9, -111, 351, -441, 274, -90, 15, -1, 0]]
DiffxTabl	[[1], [1, 0], [1, -4, 0], [1, -8, 9, 0], [1, -12, 30, -16, 0], [1, -16, 63, -80, 25, 0], [1, -20, 108, -224, 175, -36, 0], [1, -24, 165, -480, 630, -336, 49, 0], [1, -28, 234, -880, 1650, -1512, 588, -64, 0], [1, -32, 315, -1456, 3575, -4752, 3234, -960, 81, 0]]

Catalan:Inv:Rev Row sums

Trait	Seq
RowSum	[1, 1, -1, 0, 1, -1, 0, 1, -1, 0]
EvenSum	[1, 1, 1, 4, 11, 27, 72, 189, 493, 1292]
OddSum	[0, 0, -2, -4, -10, -28, -72, -188, -494, -1292]
AltSum	[1, 1, 3, 8, 21, 55, 144, 377, 987, 2584]
AbsSum	[1, 1, 3, 8, 21, 55, 144, 377, 987, 2584]
AccSum	[1, 2, -1, -2, 3, 0, -4, 4, 1, -6]
AccRevSum	[1, 1, -3, 2, 3, -7, 4, 5, -11, 6]
DiagSum	[1, 1, 1, -1, -3, -2, 3, 8, 5, -9]

Catalan:Inv:Rev Transforms

Trans	Seq
RowLcm	[1, 1, 2, 12, 60, 840, 2520, 27720, 360360, 720720]
RowGcd	[1, 1, 2, 1, 2, 1, 1, 1, 2, 1]
RowMax	[1, 1, 2, 4, 10, 21, 56, 126, 330, 792]
CentralE	[1, -2, 10, -56, 330]
CentralO	[1, -4, 21, -120, 715]
ColMiddle	[1, 1, -2, -4, 10, 21, -56, -120, 330, 715]
ColLeft	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
ColRight	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv	[1, 1, -3, -2, 21, -4, -150, 155, 1029, -2072]
InvBinConv	[1, -1, 5, -22, 101, -476, 2282, -11075, 54245, -267592]
TransSqrs	[0, 0, -2, 8, -2, -24, 40, -4, -70, 96]
TransNat0	[0, 0, -2, 2, 2, -6, 4, 4, -10, 6]
TransNat1	[1, 1, -3, 2, 3, -7, 4, 5, -11, 6]
PosHalf	[1, 2, 0, -2, 0, 2, 0, -2, 0, 2]
NegHalf	[1, -2, 8, -30, 112, -418, 1560, -5822, 21728, -81090]

Catalan:Inv:Rev Diagonals as rows

DiagRow	Seq
DiagRow0	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1	[1, -2, 3, -4, 5, -6, 7, -8, 9, -10]
DiagRow2	[1, -4, 10, -20, 35, -56, 84, -120, 165, -220]
DiagRow3	[1, -6, 21, -56, 126, -252, 462, -792, 1287, -2002]
DiagRow4	[1, -8, 36, -120, 330, -792, 1716, -3432, 6435, -11440]
DiagRow5	[1, -10, 55, -220, 715, -2002, 5005, -11440, 24310, -48620]
DiagRow6	[1, -12, 78, -364, 1365, -4368, 12376, -31824, 75582, -167960]
DiagRow7	[1, -14, 105, -560, 2380, -8568, 27132, -77520, 203490, -497420]
DiagRow8	[1, -16, 136, -816, 3876, -15504, 54264, -170544, 490314, -1307504]
DiagRow9	[1, -18, 171, -1140, 5985, -26334, 100947, -346104, 1081575, -3124550]

Catalan:Inv:Rev Diagonals as columns

DiagCol	Seq
DiagCol0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol1	[0, -2, -4, -6, -8, -10, -12, -14, -16, -18]
DiagCol2	[0, 3, 10, 21, 36, 55, 78, 105, 136, 171]
DiagCol3	[0, -4, -20, -56, -120, -220, -364, -560, -816, -1140]
DiagCol4	[0, 5, 35, 126, 330, 715, 1365, 2380, 3876, 5985]
DiagCol5	[0, -6, -56, -252, -792, -2002, -4368, -8568, -15504, -26334]
DiagCol6	[0, 7, 84, 462, 1716, 5005, 12376, 27132, 54264, 100947]
DiagCol7	[0, -8, -120, -792, -3432, -11440, -31824, -77520, -170544, -346104]
DiagCol8	[0, 9, 165, 1287, 6435, 24310, 75582, 203490, 490314, 1081575]
DiagCol9	[0, -10, -220, -2002, -11440, -48620, -167960, -497420, -1307504, -3124550]

Catalan:Inv:Rev Polynomial values as rows

PolyRow	Seq
PolyRow0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2	[1, -1, -3, -5, -7, -9, -11, -13, -15, -17]
PolyRow3	[1, 0, 5, 16, 33, 56, 85, 120, 161, 208]
PolyRow4	[1, 1, -3, -35, -119, -279, -539, -923, -1455, -2159]
PolyRow5	[1, -1, -11, 31, 305, 1111, 2869, 6119, 11521, 19855]
PolyRow6	[1, 0, 45, 160, -231, -3024, -12155, -34320, -79695, -162656]
PolyRow7	[1, 1, -91, -1079, -3263, -559, 30421, 146329, 458081, 1156897]
PolyRow8	[1, -1, 93, 3955, 26537, 80631, 102949, -220597, -1770735, -6492113]
PolyRow9	[1, 0, 85, -10064, -133551, -711704, -2227595, -4302360, -2756159, 16657264]

Catalan:Inv:Rev Polynomial values as columns

PolyCol	Seq
PolyCol0	[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyCol1	[1, 1, -1, 0, 1, -1, 0, 1, -1, 0]
PolyCol2	[1, 1, -3, 5, -3, -11, 45, -91, 93, 85]
PolyCol3	[1, 1, -5, 16, -35, 31, 160, -1079, 3955, -10064]
PolyCol4	[1, 1, -7, 33, -119, 305, -231, -3263, 26537, -133551]
PolyCol5	[1, 1, -9, 56, -279, 1111, -3024, -559, 80631, -711704]
PolyCol6	[1, 1, -11, 85, -539, 2869, -12155, 30421, 102949, -2227595]
PolyCol7	[1, 1, -13, 120, -923, 6119, -34320, 146329, -220597, -4302360]
PolyCol8	[1, 1, -15, 161, -1455, 11521, -79695, 458081, -1770735, -2756159]
PolyCol9	[1, 1, -17, 208, -2159, 19855, -162656, 1156897, -6492113, 16657264]