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A355466
Expansion of Sum_{k>=0} (k^k * x)^k/(1 - k^k * x)^(k+1).
2
1, 2, 19, 19879, 4297094601, 298028721578591321, 10314430386430205371442173873, 256923580889667562995278943476559835493321, 6277101737079381674883855772624745947410338680458857322625
OFFSET
0,2
FORMULA
E.g.f.: Sum_{k>=0} exp(k^k * x) * (k^k * x)^k/k!.
a(n) = Sum_{k=0..n} k^(k*n) * binomial(n,k).
PROG
(PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, (k^k*x)^k/(1-k^k*x)^(k+1)))
(PARI) my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*(k^k*x)^k/k!)))
(PARI) a(n) = sum(k=0, n, k^(k*n)*binomial(n, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 03 2022
STATUS
approved