A349902 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n).

1, 1, 63, 19172, 16249870, 29458152441, 97813591721181, 537081363012854224, 4535464309375188976956, 55796581668379082029481225, 958824462567528346234944706075, 22255431432328421226838750870120356, 678866987929798923743810982299237129610

Offset: 0

Author

Seiichi Manyama, Dec 05 2021

Keywords

• nonn

Crossrefs

Cf. A120485, A349885, A349889, A349891.

Programs

Mathematica

Join[{1},Table[Sum[(-1)^(n-k) k^(3n),{k,0,n}],{n,20}]] (* Harvey P. Dale, Apr 12 2022 *)

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*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) ~ 1/(1 + exp(-3)) * n^(3*n). - Vaclav Kotesovec, Dec 10 2021