A377859 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(x) ).

1, 0, 1, 2, 21, 144, 1765, 21552, 340137, 5845760, 116495721, 2550320640, 62023290109, 1642735460352, 47321500546125, 1469008742856704, 48962556079079505, 1742660440701861888, 65993849612007279697, 2648999558505185280000, 112360563741545020804581

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = exp(-x * A(x))/(1 - x*A(x)).

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

a(n) ~ phi^(3*n + 3/2) * n^(n-1) / (5^(1/4) * exp(phi*n + 1/phi)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Nov 10 2024

Prog

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

Crossrefs

Cf. A377860, A377861.

Cf. A377831.

Sequence in context: A098661 A095262 A209519 * A215710 A112673 A263435

Adjacent sequences: A377856 A377857 A377858 * A377860 A377861 A377862

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2024

Status

approved