OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..48
FORMULA
a(n) = [x^n] Sum_{k>=0} x^k/(1 - n^k*x)^(k+1).
a(n) = Sum_{k=0..n} binomial(n,k)*n^(k*(n-k)).
a(n) ~ 2^(n + 1/2) * n^(n^2/4 - 1/2) / sqrt(Pi) if n is even and a(n) ~ 2^(n + 3/2) * n^(n^2/4 - 3/4) / sqrt(Pi) if n is odd. - Vaclav Kotesovec, Jul 06 2022
MATHEMATICA
Join[{1}, Table[n! SeriesCoefficient[Sum[Exp[n^k x] x^k/k!, {k, 0, n}], {x, 0, n}], {n, 13}]]
Join[{1}, Table[SeriesCoefficient[Sum[x^k/(1 - n^k x)^(k + 1), {k, 0, n}], {x, 0, n}], {n, 13}]]
Join[{1}, Table[Sum[Binomial[n, k] n^(k (n - k)), {k, 0, n}], {n, 13}]]
PROG
(PARI) for(n=0, 20, print1(sum(k=0, n, binomial(n, k)*n^(k*(n-k))), ", ")) \\ G. C. Greubel, Nov 04 2018
(Magma) [(&+[Binomial(n, k)*n^(k*(n-k)):k in [0..n]]): n in [0..20]]; // G. C. Greubel, Nov 04 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 09 2018
STATUS
approved