A354391 Expansion of e.g.f. 1/(1 + (exp(x) - 1)^2 / 2).

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

Links

Table of n, a(n) for n=0..22.

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

Cf. A354392, A354393, A354394.

Cf. A330047, A354389, A354395.

Sequence in context: A155812 A158958 A098341 * A223173 A010292 A369756

Adjacent sequences: A354388 A354389 A354390 * A354392 A354393 A354394

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved