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A354391
Expansion of e.g.f. 1/(1 + (exp(x) - 1)^2 / 2).
5
1, 0, -1, -3, -1, 45, 269, 147, -11341, -101055, -73711, 8420247, 99423719, 87623445, -13791067291, -202300002453, -202683482821, 42194985241545, 738185254885529, 805294804942047, -216422419200618961, -4390167368672158755, -5040372451183319251
OFFSET
0,4
FORMULA
a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,2) * a(n-k).
a(n) = Sum_{k=0..floor(n/2)} (2*k)! * Stirling2(n,2*k)/(-2)^k.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(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, j)*stirling(j, 2, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\2, (2*k)!*stirling(n, 2*k, 2)/(-2)^k);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 25 2022
STATUS
approved