A356634 - OEIS

%I #11 Aug 19 2022 09:25:56

%S 1,1,2,6,24,125,780,5670,47040,439110,4561200,52182900,651974400,

%T 8832874050,129001672800,2020822303500,33805804032000,601587281295000,

%U 11348960759136000,226275153994890000,4755046903326720000,105061084389756495000,2435176811445618240000

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

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

%t 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 *)

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

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

%Y Cf. A356632, A356633.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 18 2022