You have an N by N board. Write a function that, given N, returns the number of possible arrangements of the board where N queens can be placed on the board without threatening each other, i.e. no two queens share the same row, column, or diagonal.

The following are the first 7 terms of the sequence (from Wikipedia's Eight queens puzzle page):

>>> [coding_problem_38(n + 1) for n in range(7)]
[1, 0, 0, 2, 10, 4, 40]