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A113750 Consider the generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next k multiples of n-1, n-2, ..., 1, for n>=1. Now construct the array, t, such that t(n,k) is the n-th and successively rounding up to the next k multiples. This sequence is the determinant of that array.

%I A113750 #6 Mar 30 2012 18:36:52
%S A113750 2,2,-4,0,-32,-256,-512,-5632,-180736,-135168,-61440,5529600,
%T A113750 -1554161664,17735712768,351786369024,-79390588010496,
%U A113750 -1755801711804416,-30318369806745600,-4162409018839531520,528913148312239996928
%N A113750 Consider the generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next k multiples of n-1, n-2, ..., 1, for n>=1. Now construct the array, t, such that t(n,k) is the n-th and successively rounding up to the next k multiples. This sequence is the determinant of that array.
%t A113750 f[n_, k_] := Fold[ #2*Ceiling[ #1/#2 + k] &, n, Reverse@Range[n - 1]]; Table[Det[Table[f[i, j], {i, 2, n}, {j, 0, n - 2}]], {n, 2, 21}]
%K A113750 sign
%O A113750 2,1
%A A113750 _Paul D. Hanna_ and _Robert G. Wilson v_, Nov 05 2005