A379702 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) / (1 + x*exp(3*x)) ).

1, 0, 5, 11, 333, 2829, 78553, 1360197, 42149817, 1123709129, 40775629581, 1453036152897, 62005204699045, 2736440768515869, 135913168259011809, 7106229274104610829, 405068417020871464689, 24398077807975709138193, 1574189366334360310720405

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = (n!/(n+1)) * Sum_{k=0..n} (2*n-3*k-1)^k * binomial(n+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*n-3*k-1)^k*binomial(n+1, n-k)/k!)/(n+1);

Crossrefs

Cf. A108919, A379701.

Cf. A366233.

Sequence in context: A266517 A228054 A283354 * A156330 A056253 A101832

Adjacent sequences: A379699 A379700 A379701 * A379703 A379704 A379705

Keyword

nonn

Author

Seiichi Manyama, Dec 30 2024

Status

approved