A352693 Expansion of e.g.f. 1 / (1 - Sum_{k>=1} sigma_2(k) * x^k/k!).

1, 1, 7, 46, 455, 5406, 78172, 1312116, 25214479, 544777183, 13080808752, 345471545728, 9953804592152, 310687941345796, 10443489230611052, 376122782541917166, 14449157656748079247, 589772212576633845886, 25488817336672959449725

Offset: 0

Author

Seiichi Manyama, Mar 29 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..393

Crossrefs

Cf. A340903, A340904.

Cf. A001157, A320649, A352694.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, sigma(k, 2)*x^k/k!))))

PARI

a(n) = if(n==0, 1, sum(k=1, n, sigma(k, 2)*binomial(n, k)*a(n-k)));

Formula

a(0) = 1; a(n) = Sum_{k=1..n} sigma_2(k) * binomial(n,k) * a(n-k).