A377861 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(x) ).

1, 2, 15, 206, 4193, 113904, 3882511, 159475280, 7672503681, 423360926720, 26362968645071, 1829066086810368, 139929538526047585, 11703312997355442176, 1062423600515479191375, 104042389901715413633024, 10933256593926589800851969, 1227201235266954603172331520

Offset

0,2

Links

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

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = exp(-x * A(x))/(1 - x*A(x))^3.

a(n) = n! * Sum_{k=0..n} (-1)^k * (n+1)^(k-1) * binomial(4*n-k+2,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (-1)^k*(n+1)^(k-1)*binomial(4*n-k+2, n-k)/k!);

Crossrefs

Cf. A377859, A377860.

Cf. A377833.

Sequence in context: A351501 A124558 A020565 * A282521 A099718 A143881

Adjacent sequences: A377858 A377859 A377860 * A377862 A377863 A377864

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2024

Status

approved