akiyama-tanigawa_numerators.sf

#!/usr/bin/ruby

# The unreduced numerators produced by the Akiyama–Tanigawa algorithm.

# The corresponding unreduced denominators are:
#   https://oeis.org/A064320

# Example:
#   bernoulli(n) = akiyama_tanigawa_numerator(n) / Prod_{k=2..n+1} k^binomial(n, k-1)

func akiyama_tanigawa_numerator(n) {
    n.bernfrac * prod(2..(n+1), {|k| k**binomial(n, k-1) })
}

for n in (0..10 -> by(2)) {
    say "A(#{n}) = #{akiyama_tanigawa_numerator(n).abs.factor_exp} = #{akiyama_tanigawa_numerator(n)}"
}

__END__
A(0)  = []                                       = 1
A(2)  = [[2,   1]]                               = 2
A(4)  = [[2,  11], [3,   5]]                     = -497664
A(6)  = [[2,  51], [3,  20], [5,  15]]           = 239609999527967195136000000000000000
A(8)  = [[2, 199], [3,  85], [5,  69], [7,  28]] = -22488019432655947294586954838400753261235046040984100580870030674321006065067975174876421496694774956032000000000000000000000000000000000000000000000000000000000000000000000
A(10) = [[2, 871], [3, 386], [5, 221], [7, 210]] = 20365257530918016171039056001495283122906935375511621880937985285541368957251236512682327909990112153849262228719316998217599272439458747323536731851414642636432448263703122571698861175490069815698104764675945775839382072046627151681800069326017346945224612080463443188802561045025518519287776438753210636201461443257757332000981973116850724254395705822262814809408842731863277702200645974274119109818626996367781903697874837091937872569655899718801790772307704771607635081669632024064847422349647168621736312036578982794202420561798986849926832723350414950400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000