A379847 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(3*x)) ).

1, 2, 17, 259, 5773, 171021, 6342937, 283094309, 14785425081, 885090944809, 59765476266061, 4494836808752049, 372655043070926821, 33769844474642217293, 3320996349535681398849, 352267766021524028011981, 40091829710459334010532593, 4873329774181782935197522641

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (n!/(n+1)) * Sum_{k=0..n} (4*n-3*k+1)^k * binomial(n+1,n-k)/k!.

E.g.f. A(x) satisfies A(x) = exp(x*A(x)) / ( 1 - x*exp(4*x*A(x)) ). - Seiichi Manyama, Feb 04 2025

Prog

(PARI) a(n) = n!*sum(k=0, n, (4*n-3*k+1)^k*binomial(n+1, n-k)/k!)/(n+1);

Crossrefs

Cf. A088690, A379456, A379846.

Cf. A366233, A379702.

Sequence in context: A291206 A037896 A099714 * A301584 A387967 A195443

Adjacent sequences: A379844 A379845 A379846 * A379848 A379849 A379850

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2025

Status

approved