OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..214
FORMULA
a(n) ~ n^(2*n). - Vaclav Kotesovec, May 31 2019
From Seiichi Manyama, Jul 04 2022: (Start)
G.f.: Sum_{k>=0} (k^2 * x)^k/(1 - x)^(k+1).
E.g.f.: exp(x) * Sum_{k>=0} (k^2 * x)^k/k!. (End)
MATHEMATICA
Table[1 + Sum[Binomial[n, k]*k^(2*k), {k, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, May 31 2019 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)*k^(2*k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1-x)^(k+1))) \\ Seiichi Manyama, Jul 04 2022
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, (k^2*x)^k/k!))) \\ Seiichi Manyama, Jul 04 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 12 2019
STATUS
approved