A352842 Expansion of e.g.f. exp(Sum_{k>=1} sigma_k(k) * x^k).

1, 1, 11, 199, 7585, 427961, 37901851, 4526311231, 729098029409, 149311985624785, 38243144308952971, 11913301283967428951, 4445712423354285230401, 1954806416110914007773769, 1000799932457357582959443035, 589931632494798210345741193231

Offset: 0

Author

Seiichi Manyama, Apr 05 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..232

Crossrefs

Cf. A294363, A294361, A294362.

Programs

Mathematica

nmax = 20; CoefficientList[Series[E^(Sum[DivisorSigma[k, k]*x^k, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2022 *)

PARI

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

PARI

a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, k*sigma(k, k)*a(n-k)/(n-k)!));

Formula

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

a(n) ~ n! * n^n. - Vaclav Kotesovec, Apr 15 2022