A354135 Expansion of e.g.f. 1/(1 - log(1 + x)^5/120).

1, 0, 0, 0, 0, 1, -15, 175, -1960, 22449, -269073, 3403070, -45510630, 643152796, -9586136560, 150319669136, -2473024029840, 42562037379744, -764017130370276, 14260496108114340, -275877454002406236, 5512350021871343616, -113318466860425703184

Offset

0,7

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * Stirling1(k,5) * a(n-k).

a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling1(n,5*k)/120^k.

Prog

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

Crossrefs

Cf. A006252, A354134.

Cf. A346920, A346924.

Sequence in context: A346320 A051588 A016164 * A354137 A000482 A347004

Adjacent sequences: A354132 A354133 A354134 * A354136 A354137 A354138

Keyword

sign

Author

Seiichi Manyama, May 18 2022

Status

approved