A379864 Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-x) - x)^2 ).

1, 4, 54, 1334, 48816, 2383682, 146036788, 10781227690, 932243805168, 92452039842626, 10346916215343564, 1290195352404492602, 177396099439904780200, 26665611450484642809058, 4350590232650155748720484, 765717105431099707449714218

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)) - x*A(x))^2.

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379867.

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

Prog

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

Crossrefs

Cf. A379867.

Sequence in context: A138459 A111161 A216733 * A203039 A369569 A201731

Adjacent sequences: A379861 A379862 A379863 * A379865 A379866 A379867

Keyword

nonn,new

Author

Seiichi Manyama, Jan 04 2025

Status

approved