A349901 a(n) = Sum_{k=0..n} k^(3*n).

1, 1, 65, 20196, 17312754, 31605701625, 105443761093411, 580964060390826448, 4918745981990731659972, 60634331963604550954204425, 1043651859661187698792930519525, 24256699178432730349549665042311076, 740737411098120942914045235001015624310

Offset: 0

Author

Seiichi Manyama, Dec 05 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..152

Crossrefs

Cf. A249459, A349883, A349886.

Programs

PARI

a(n) = sum(k=0, n, k^(3*n));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1-k^3*x)))

Formula

G.f.: Sum_{k>=0} (k^3 * x)^k/(1 - k^3 * x).

a(n) ~ exp(3)/(exp(3)-1) * n^(3*n). - Vaclav Kotesovec, Dec 05 2021