A380664 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x/(1 - x)^2) ).

1, 2, 17, 268, 6277, 196416, 7716109, 365398496, 20271580137, 1290027358720, 92653747607401, 7414981595716608, 654373744057368493, 63136350047908917248, 6612064512998173129125, 747016321343021395603456, 90564758322246657646854481, 11727981253987656671672008704

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))^2)/(1 - x*A(x)).

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

Prog

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

Crossrefs

Cf. A377831, A380663.

Cf. A361598.

Sequence in context: A379847 A301584 A195443 * A176585 A086534 A198287

Adjacent sequences: A380658 A380659 A380663 * A380665 A380666 A380667

Keyword

nonn,new

Author

Seiichi Manyama, Jan 30 2025

Status

approved