A379662 Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-3*x) - x) ).

1, 4, 55, 1407, 53697, 2743893, 176247927, 13657260501, 1240444335969, 129281173193385, 15210977483374479, 1994549350608453609, 288445997202717914433, 45611213861740547292093, 7829287622920723803498279, 1449907335654700964735333997, 288151338120152032299063196737

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A377890, A379661.

Sequence in context: A322627 A206384 A380919 * A271715 A099122 A001500

Adjacent sequences: A379659 A379660 A379661 * A379663 A379664 A379665

Keyword

nonn

Author

Seiichi Manyama, Dec 29 2024

Status

approved