A376124 E.g.f. A(x) satisfies A(x) = x * exp(A(x)) * (1 + 3*A(x)).

0, 1, 8, 117, 2584, 77245, 2923776, 134147881, 7237959296, 449153207001, 31518672486400, 2468063119978621, 213353171897306112, 20181854221412587093, 2073632053555295657984, 229977288184566078752625, 27382787929802599713243136, 3483970698377702965413968689

Offset

0,3

Links

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

Index entries for reversions of series

Formula

E.g.f.: Series_Reversion( x * exp(-x) / (1 + 3*x) ).

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

a(n) ~ ((7 + sqrt(13))/2)^n * n^(n-1) / (13^(1/4) * exp((7 - sqrt(13))*n/6)). - Vaclav Kotesovec, Sep 11 2024

Prog

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

Crossrefs

Cf. A052885, A376123.

Cf. A376094, A376101.

Sequence in context: A056988 A085699 A046914 * A364984 A341197 A342182

Adjacent sequences: A376121 A376122 A376123 * A376125 A376126 A376127

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2024

Status

approved