A376443 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1))^2 ).

1, 0, 0, 12, 0, 120, 10800, 1680, 766080, 55913760, 48686400, 12973625280, 878369184000, 2257312337280, 475877474392320, 31178226637958400, 176135891323392000, 32566007822802854400, 2111180034178805990400, 22027962609483730099200, 3749400628293386626560000, 244391453278125083388057600

Offset

0,4

Links

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

Index entries for reversions of series

Formula

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

a(n) = (2 * n!/(2n+2)!) * Sum_{k=0..floor(n/2)} (3*n-2*k+1)! * Stirling2(k,n-2*k)/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^2)/x))
(PARI) a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*stirling(k, n-2*k, 2)/k!)/(2*n+2)!;

Crossrefs

Cf. A376345, A376444.

Cf. A375664.

Sequence in context: A257949 A375664 A375680 * A376441 A077351 A370018

Adjacent sequences: A376440 A376441 A376442 * A376444 A376445 A376446

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2024

Status

approved