A364940 E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x*A(x))^3 ).

1, 1, 9, 124, 2525, 68616, 2338357, 96004672, 4616135001, 254542038400, 15839013320801, 1098078537291264, 83940831427695541, 7014958697801657344, 636298582947212386125, 62261039244978489081856, 6537251350698278868150833, 733159568772947522820538368

Offset: 0

Author

Seiichi Manyama, Aug 14 2023

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A052873, A364939.

Cf. A091695.

Programs

PARI

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

Formula

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

E.g.f.: (1/x) * Series_Reversion( x*exp(-x/(1 - x)^3) ). - Seiichi Manyama, Sep 23 2024