A293849 - OEIS

A293849

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

%I #19 Apr 17 2022 22:07:44

%S 1,1,5,67,1825,85661,6208861,643969495,90484635137,16538699920825,

%T 3811890603086101,1081079416534448651,369888779067183276385,

%U 150214056908992952336917,71424576855634502660684525,39304140073887410352909383071

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

%H Seiichi Manyama, <a href="/A293849/b293849.txt">Table of n, a(n) for n = 0..232</a>

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

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

%F a(n) ~ n! * n^(n-1). - _Vaclav Kotesovec_, Oct 18 2017

%t 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 *)

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

%Y Cf. A293848.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 17 2017