A352659 a(n) = n! * Sum_{k=0..floor(n/3)} 1 / (3*k)!.

1, 1, 2, 7, 28, 140, 841, 5887, 47096, 423865, 4238650, 46625150, 559501801, 7273523413, 101829327782, 1527439916731, 24439038667696, 415463657350832, 7478345832314977, 142088570813984563, 2841771416279691260, 59677199741873516461, 1312898394321217362142

Offset: 0

Author

Ilya Gutkovskiy, Mar 25 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000522, A009179, A087350, A143819, A348597, A352660.

Programs

Mathematica

Table[n! Sum[1/(3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(Exp[x] + 2 Exp[-x/2] Cos[Sqrt[3] x/2])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

PARI

a(n) = n! * sum(k=0, n\3, 1/(3*k)!); \\ Michel Marcus, Mar 29 2022

Formula

E.g.f.: (exp(x) + 2 * exp(-x/2) * cos(sqrt(3)*x/2)) / (3*(1 - x)).

a(n) = floor(c * n!), where c = 1.16805831... = A143819.