A323280 a(n) = Sum_{k=0..n} binomial(n,k) * k^(2*k).

1, 2, 19, 781, 68553, 10100761, 2236373953, 693667946945, 286962262702657, 152652510206521921, 101513694573289791441, 82511051259976074269425, 80480313356721971865934369, 92773167329045961244649105633, 124768226258051318899374299271601

Offset

0,2

Links

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

Formula

a(n) ~ n^(2*n). - Vaclav Kotesovec, May 31 2019

From Seiichi Manyama, Jul 04 2022: (Start)

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

E.g.f.: exp(x) * Sum_{k>=0} (k^2 * x)^k/k!. (End)

Mathematica

Table[1 + Sum[Binomial[n, k]*k^(2*k), {k, 1, n}], {n, 0, 15}] (* Vaclav Kotesovec, May 31 2019 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*k^(2*k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^k/(1-x)^(k+1))) \\ Seiichi Manyama, Jul 04 2022
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, (k^2*x)^k/k!))) \\ Seiichi Manyama, Jul 04 2022

Crossrefs

Cf. A062206, A064570, A086331, A242446, A277454, A277456, A308490, A316747.

Sequence in context: A013047 A012951 A012980 * A013110 A024228 A015191

Adjacent sequences: A323277 A323278 A323279 * A323281 A323282 A323283

Keyword

nonn

Author

Seiichi Manyama, Jan 12 2019

Status

approved