A354394 Expansion of e.g.f. 1/(1 + (exp(x) - 1)^5 / 120).

1, 0, 0, 0, 0, -1, -15, -140, -1050, -6951, -42273, -232870, -949740, 2401399, 149618469, 2979464124, 47639256210, 683529622229, 9045426379611, 109599657976942, 1148191101672384, 8033814119097459, -50834295574038207, -3977581842278623216, -119536187842156328034

Offset

0,7

Links

Table of n, a(n) for n=0..24.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,5) * a(n-k).

a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k)/(-120)^k.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(exp(x)-1)^5/120)))
(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, 5, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2)/(-120)^k);

Crossrefs

Cf. A354391, A354392, A354393.

Cf. A346896, A346924, A354398.

Sequence in context: A133716 A035330 A002803 * A346977 A354398 A056281

Adjacent sequences: A354391 A354392 A354393 * A354395 A354396 A354397

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved