A375656 Expansion of e.g.f. exp(x^3 + x * exp(x^3/6)).

1, 1, 1, 7, 29, 81, 541, 3781, 18537, 129529, 1171961, 8446131, 66198661, 683784817, 6492131829, 59303102041, 664191218321, 7659196889841, 82391350746097, 991483941558079, 13066764825298221, 164001743446274161, 2139651772557011021, 30946063565684912877

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

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

Crossrefs

Cf. A080108, A375655.

Cf. A375634.

Sequence in context: A231988 A141854 A267290 * A079796 A242727 A229795

Adjacent sequences: A375653 A375654 A375655 * A375657 A375658 A375659

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2024

Status

approved