A356608 a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(24^k * (n - 4*k)!).

1, 1, 1, 1, 1, 6, 31, 106, 281, 1261, 13861, 106261, 558361, 2709136, 32802771, 447762316, 4093711441, 28011714641, 293624974441, 5549250905281, 80454378591121, 815886496908946, 8379058314620071, 168672787637953446, 3514729162490432041, 51656083670790267901

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..455

Crossrefs

Cf. A354436, A356029, A356328.

Cf. A354552, A356630, A356634.

Programs

Mathematica

a[n_] := n! * Sum[(n - 4*k)^k/(24^k*(n - 4*k)!), {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 26, 0] (* Amiram Eldar, Aug 19 2022 *)

PARI

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

PARI

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

Formula

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