A293849 Expansion of e.g.f.: exp(Sum_{n>=1} n^(n-1)*x^n).

1, 1, 5, 67, 1825, 85661, 6208861, 643969495, 90484635137, 16538699920825, 3811890603086101, 1081079416534448651, 369888779067183276385, 150214056908992952336917, 71424576855634502660684525, 39304140073887410352909383071

Offset: 0

Author

Seiichi Manyama, Oct 17 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A293848.

Programs

Mathematica

nmax = 20; CoefficientList[Series[E^Sum[k^(k-1)*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)

PARI

{a(n) = n!*polcoeff(exp(sum(k=1, n, k^(k-1)*x^k)+x*O(x^n)), n)}

Formula

E.g.f.: exp(Sum_{n>=1} n^(n-1)*x^n).

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k^k*a(n-k)/(n-k)! for n > 0.

a(n) ~ n! * n^(n-1). - Vaclav Kotesovec, Oct 18 2017