A376094 E.g.f. A(x) satisfies A(x) = x * exp(3*A(x)) * (1 + A(x)).

0, 1, 8, 141, 3912, 148845, 7210368, 424596753, 29451533184, 2352033716409, 212561497036800, 21446708257599669, 2389752470910624768, 291465187429985987301, 38621040916534872219648, 5524829459141297215253625, 848620611495100582915571712

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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

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

a(n) ~ ((5 + sqrt(21))/2)^n * n^(n-1) / (3^(3/4) * 7^(1/4) * exp((5 - sqrt(21))*n/2)). - Vaclav Kotesovec, Sep 10 2024

Prog

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

Crossrefs

Cf. A052885, A376093.

Sequence in context: A224735 A090931 A367199 * A239757 A295242 A305763

Adjacent sequences: A376091 A376092 A376093 * A376095 A376096 A376097

Keyword

nonn

Author

Seiichi Manyama, Sep 10 2024

Status

approved