A376475 E.g.f. satisfies A(x) = exp( x^3*A(x)^3 / (1 - x*A(x)) ).

1, 0, 0, 6, 24, 120, 3240, 45360, 584640, 13668480, 322963200, 7224940800, 201040963200, 6254004556800, 197219089267200, 6845849673062400, 260976932536320000, 10410615332941824000, 441056225586706329600, 20015606466369626112000, 955852013167308601344000, 47944066629381635801088000

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Index entries for reversions of series

Formula

E.g.f.: (1/x) * Series_Reversion( x*exp(-x^3 / (1 - x)) ).

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

Prog

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

Crossrefs

Cf. A052873, A376474.

Cf. A293049.

Sequence in context: A052557 A376516 A376495 * A357192 A357194 A188232

Adjacent sequences: A376472 A376473 A376474 * A376476 A376477 A376478

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2024

Status

approved