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A355466 Expansion of Sum_{k>=0} (k^k * x)^k/(1 - k^k * x)^(k+1).

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%I A355466 #12 Jul 03 2022 09:34:40
%S A355466 1,2,19,19879,4297094601,298028721578591321,
%T A355466 10314430386430205371442173873,
%U A355466 256923580889667562995278943476559835493321,6277101737079381674883855772624745947410338680458857322625
%N A355466 Expansion of Sum_{k>=0} (k^k * x)^k/(1 - k^k * x)^(k+1).
%F A355466 E.g.f.: Sum_{k>=0} exp(k^k * x) * (k^k * x)^k/k!.
%F A355466 a(n) = Sum_{k=0..n} k^(k*n) * binomial(n,k).
%o A355466 (PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, (k^k*x)^k/(1-k^k*x)^(k+1)))
%o A355466 (PARI) my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*(k^k*x)^k/k!)))
%o A355466 (PARI) a(n) = sum(k=0, n, k^(k*n)*binomial(n, k));
%Y A355466 Cf. A072034, A242446, A355470.
%Y A355466 Cf. A349886.
%K A355466 nonn
%O A355466 0,2
%A A355466 _Seiichi Manyama_, Jul 03 2022