A376123 E.g.f. A(x) satisfies A(x) = x * exp(A(x)) * (1 + 2*A(x)).

0, 1, 6, 69, 1216, 29145, 886176, 32692597, 1419067392, 70867571409, 4002985561600, 252350116482981, 17564151708647424, 1337849793390444841, 110694246048458612736, 9886625352559043695125, 948044647019001482838016, 97146789899768662622795553

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 + 2*x) ).

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

a(n) = n * A088692(n-1).

a(n) ~ 2^(2*n) * n^(n-1) / (sqrt(3) * exp(n/2)). - Vaclav Kotesovec, Sep 11 2024

Prog

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

Crossrefs

Cf. A052885, A376124.

Cf. A088692, A376093, A376100.

Sequence in context: A349556 A381479 A364982 * A381175 A098639 A305110

Adjacent sequences: A376120 A376121 A376122 * A376124 A376125 A376126

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2024

Status

approved