A249459 a(n) = Sum_{k=0..n} k^(2*n).

1, 1, 17, 794, 72354, 10874275, 2438235715, 762963987380, 317685943157892, 169842891165484965, 113394131858832552133, 92465351109879998121806, 90431265068257318469676710, 104479466717230437574945525959, 140782828210237288756752539959687

Offset: 0

Author

Vaclav Kotesovec, Oct 29 2014

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..214

Crossrefs

Cf. A031971, A224899, A249489.

Programs

Mathematica

Table[Sum[k^(2*n),{k,1,n}],{n,1,20}]
Table[n!*SeriesCoefficient[Sum[Exp[k^2*x], {k, 1, n}],{x,0,n}], {n,1,20}]

PARI

a(n)=n!*polcoeff(sum(k=0, n, exp(k*x+x*O(x^n))^k), n);
for(n=1, 20, print1(a(n), ", "))

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1-k^2*x))) \\ Seiichi Manyama, Dec 03 2021

Formula

E.g.f.: Sum_{n>=0} exp(n^2*x).

a(n) ~ exp(2)/(exp(2)-1) * n^(2*n).

G.f.: Sum_{k>=0} (k^2 * x)^k/(1 - k^2 * x). - Seiichi Manyama, Dec 03 2021

Extensions

a(0)=1 prepended by Seiichi Manyama, Dec 03 2021