A354393 Expansion of e.g.f. 1/(1 + (exp(x) - 1)^4 / 24).

1, 0, 0, 0, -1, -10, -65, -350, -1631, -5250, 18395, 685850, 10485739, 127737610, 1336804105, 11432407350, 54280609109, -712071643930, -29671691715185, -660215774400350, -11770593620859521, -176475952496559870, -2055362595355830475, -9749893741512339250

Offset

0,6

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,4) * a(n-k).

a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling2(n,4*k)/(-24)^k.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(exp(x)-1)^4/24)))
(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, 4, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 2)/(-24)^k);

Crossrefs

Cf. A354391, A354392, A354394.

Cf. A346895, A354390, A354397.

Sequence in context: A073381 A092441 A022638 * A346976 A354397 A003519

Adjacent sequences: A354390 A354391 A354392 * A354394 A354395 A354396

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved