A356634 a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/24^k.

1, 1, 2, 6, 24, 125, 780, 5670, 47040, 439110, 4561200, 52182900, 651974400, 8832874050, 129001672800, 2020822303500, 33805804032000, 601587281295000, 11348960759136000, 226275153994890000, 4755046903326720000, 105061084389756495000, 2435176811445618240000

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Crossrefs

Cf. A356632, A356633.

Programs

Mathematica

a[n_] := n! * Sum[(n - 4*k)^k/24^k, {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 23, 0] (* Amiram Eldar, Aug 19 2022 *)

PARI

a(n) = n!*sum(k=0, n\4, (n-4*k)^k/24^k);

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^4/24))))

Formula

E.g.f.: Sum_{k>=0} x^k / (1 - k*x^4/24).