A356633 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/6^k.

1, 1, 2, 6, 28, 160, 1080, 8540, 78400, 816480, 9492000, 122337600, 1736380800, 26930904000, 453515462400, 8254694448000, 161734564992000, 3397235761920000, 76228261933824000, 1821644243362944000, 46233794313907200000, 1242946827521118720000

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Crossrefs

Cf. A356632, A356634.

Cf. A352946.

Programs

Mathematica

a[n_] := n! * Sum[(n - 3*k)^k/6^k, {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)

PARI

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

PARI

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

Formula

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