A349889 a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(2*n).

1, 1, 15, 666, 59230, 8775075, 1948891581, 605698755508, 250914820143996, 133610836793706405, 88919025666286620475, 72317513878698256697166, 70571883548815735717843290, 81383769918571603591381635271

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

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

a(n) ~ 1/(1 + exp(-2)) * n^(2*n). - Vaclav Kotesovec, Dec 10 2021

Mathematica

Join[{1}, Table[Sum[(-1)^(n-k) k^(2n), {k, 0, n}], {n, 20}]] (* Harvey P. Dale, Nov 19 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k^(2*n));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1+k^2*x)))

Crossrefs

Cf. A120485, A249459, A349884, A349891, A349902.

Sequence in context: A280179 A223203 A279465 * A279531 A079600 A171113

Adjacent sequences: A349886 A349887 A349888 * A349890 A349891 A349892

Keyword

nonn

Author

Seiichi Manyama, Dec 04 2021

Status

approved