A375586 Expansion of e.g.f. 1 / (1 + x - x * exp(x^2/2)).
1, 0, 0, 3, 0, 15, 180, 105, 5040, 46305, 132300, 3752595, 33679800, 243378135, 5565940380, 56191160025, 712410098400, 14889814164225, 183558878603100, 3236148386145675, 66650136566013000, 1027807726886515575, 21983938825036488300, 469896981350215644225
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2/2)))) -
PARI
a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 2)/(2^k*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(k,n-2*k)/(2^k*k!).