A354395 Expansion of e.g.f. exp( -(exp(x) - 1)^2 / 2 ).
1, 0, -1, -3, -4, 15, 149, 672, 1091, -12855, -162796, -1060653, -2925319, 30881760, 598929239, 5688937797, 29126981516, -112222099065, -4930674413971, -69798552313728, -598032658869829, -1296500625378255, 65193402297999524, 1515140106814565547
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(exp(x)-1)^2/2))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i-1, j-1)*stirling(j, 2, 2)*v[i-j+1])); v;
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PARI
a(n) = sum(k=0, n\2, (2*k)!*stirling(n, 2*k, 2)/((-2)^k*k!));
Formula
a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,2) * a(n-k).
a(n) = Sum_{k=0..floor(n/2)} (2*k)! * Stirling2(n,2*k)/((-2)^k * k!).