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A355464
Expansion of Sum_{k>=0} x^k/(1 - k^k * x)^(k+1).
3
1, 2, 4, 17, 210, 9217, 1399298, 811229225, 2071392232962, 20710319937493889, 1137259214532706572162, 255141201504146525745627265, 348787971214016591166179037803522, 2262996819897931095524655885144485185409
OFFSET
0,2
FORMULA
E.g.f.: Sum_{k>=0} exp(k^k * x) * x^k/k!.
a(n) = Sum_{k=0..n} k^(k*(n-k)) * binomial(n,k).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^k*x)^(k+1)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*x^k/k!)))
(PARI) a(n) = sum(k=0, n, k^(k*(n-k))*binomial(n, k));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 03 2022
STATUS
approved