A354137 Expansion of e.g.f. exp(log(1 + x)^5/120).

1, 0, 0, 0, 0, 1, -15, 175, -1960, 22449, -269199, 3410000, -45753180, 650179816, -9771920158, 155020385156, -2589888417480, 45461879164584, -836540418765834, 16099972965770778, -323385447259166454, 6764948641797695496, -147088325599708573080

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-1,k-1) * Stirling1(k,5) * a(n-k).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(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-1, j-1)*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*k!));

Crossrefs

Cf. A354136.

Cf. A327506, A347004, A354135.

Sequence in context: A051588 A016164 A354135 * A000482 A347004 A346947

Adjacent sequences: A354134 A354135 A354136 * A354138 A354139 A354140

Keyword

sign

Author

Seiichi Manyama, May 18 2022

Status

approved