A375395 Expansion of e.g.f. 1 / (exp(-x^3/6) - x).

1, 1, 2, 7, 32, 180, 1210, 9520, 85680, 867160, 9749600, 120582000, 1626994600, 23782158400, 374367193200, 6314037129400, 113591474796800, 2171267969270400, 43944509528920000, 938808209417478400, 21111813400597920000, 498498097342637392000

Offset: 0

Author

Seiichi Manyama, Aug 21 2024

Keywords

• nonn

Crossrefs

Cf. A072597, A375394.

Programs

Maple

A375395 := proc(n)
    n!*add(((n-3*k+1)/6)^k/k!,k=0..floor(n/3)) ;
end proc:
seq(A375395(n),n=0..60) ; # R. J. Mathar, Aug 23 2024

PARI

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

PARI

a(n) = n!*sum(k=0, n\3, ((n-3*k+1)/6)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} ((n-3*k+1)/6)^k/k!.