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%I #13 Feb 22 2015 23:27:03
%S 1,-1,-4,-21,-160,-1505,-17136,-226093,-3334528,-53031105,-864640000,
%T -12957006821,-107329453056,4548002439071,409321789829120,
%U 23780752998703875,1257249577352658944,65336038911885770623
%N det(I - M) where M_jk = (j*x)^k/k!.
%C The n X n matrix M is a Vandermonde matrix of (x, 2x, 3x, ..., j*x, ..., n*x) scaled by factorials. The first n coefficients of x in det(I - M) are always the same.
%H Andrew J. Robbins, <a href="/A157503/b157503.txt">Table of n, a(n) for n = 0..50</a>
%F E.g.f.: det(I - M) where M_jk = (j*x)^k/k!.
%t A[n_] := D[Det[Table[KroneckerDelta[j,k] - (j*x)^k/k!, {j,1,n}, {k,1,n}]], {x, n}]/.x->0
%K easy,sign
%O 0,3
%A _Andrew J. Robbins_, Mar 02 2009