A349891 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*n).

1, 0, 16, 19619, 4294436111, 298022124379673232, 10314423867168242405282727694, 256923577039829077600620024397823949901879, 6277101735175093150055816289268196664555481440709896684157

Offset: 0

Author

Seiichi Manyama, Dec 04 2021

Keywords

• nonn

Crossrefs

Cf. A120485, A349886, A349889.

Programs

PARI

a(n) = sum(k=0, n, (-1)^(n-k)*k^(k*n));

PARI

my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, k^k^2*x^k/(1+k^k*x)))

Formula

G.f.: Sum_{k>=0} k^(k^2) * x^k/(1 + k^k * x).

a(n) ~ n^(n^2). - Vaclav Kotesovec, Dec 10 2021