A306628 Expansion of e.g.f. log(Sum_{k>=0} (k*x)^k).

1, 7, 140, 5394, 336024, 30663840, 3846629520, 634415055120, 133073632016640, 34596321663980160, 10919217470376902400, 4113179201266142515200, 1822997615295693513600000, 939158618068666181592806400, 556530141861219809204393472000

Offset: 1

Author

Seiichi Manyama, Mar 01 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..232

Crossrefs

Cf. A000142, A000312, A122949.

Programs

Mathematica

nmax = 20; Rest[CoefficientList[Series[Log[1 + Sum[(k*x)^k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Mar 02 2019 *)

PARI

N=20; x='x+O('x^N); Vec(serlaplace(log(sum(k=0, N, (k*x)^k))))

Formula

a(n) ~ n! * n^n. - Vaclav Kotesovec, Mar 02 2019