A356328 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * (n - 3*k)!).

1, 1, 1, 1, 5, 21, 61, 281, 2521, 15625, 84841, 971521, 10646461, 83366141, 962405445, 15445935961, 181502928881, 2182235585041, 42297481449361, 714940186390465, 10007476059187381, 204722588272279141, 4600003555996715021, 80767827313930590681

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Crossrefs

Cf. A354436, A356029, A356608.

Cf. A354551, A356629, A356633.

Programs

Mathematica

a[n_] := n! * Sum[(n - 3*k)^k/(6^k*(n - 3*k)!), {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 24, 0] (* Amiram Eldar, Aug 19 2022 *)

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*(n-3*k)!));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^3/6)))))

Formula

E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^3/6)).