A355466 - OEIS

%I #12 Jul 03 2022 09:34:40

%S 1,2,19,19879,4297094601,298028721578591321,

%T 10314430386430205371442173873,

%U 256923580889667562995278943476559835493321,6277101737079381674883855772624745947410338680458857322625

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

%F E.g.f.: Sum_{k>=0} exp(k^k * x) * (k^k * x)^k/k!.

%F a(n) = Sum_{k=0..n} k^(k*n) * binomial(n,k).

%o (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 (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 (PARI) a(n) = sum(k=0, n, k^(k*n)*binomial(n, k));

%Y Cf. A072034, A242446, A355470.

%Y Cf. A349886.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 03 2022