A352841 Expansion of e.g.f. 1/(1 - Sum_{k>=1} sigma_k(k) * x^k/k!).

1, 1, 7, 64, 851, 13906, 277972, 6466650, 172651643, 5186830537, 173327806752, 6373233407498, 255743444526584, 11119651415719744, 520752884139087852, 26132341317365562754, 1398900109763305183707, 79569524691656775423766

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, sigma(k, k)*x^k/k!))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, sigma(k, k)*binomial(n, k)*a(n-k)));

Crossrefs

Cf. A340903, A340904, A352693.

Cf. A023887, A352839, A352843.

Sequence in context: A197785 A360465 A252654 * A197787 A024095 A274823

Adjacent sequences: A352838 A352839 A352840 * A352842 A352843 A352844

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2022

Status

approved