A377546 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x))^2 ).

1, 2, 18, 294, 7136, 231410, 9421932, 462459242, 26593896912, 1754278123266, 130611457831700, 10835721949072922, 991315043401627320, 99154012317212577218, 10765112531819005907484, 1260860266373297376720810, 158473050112495481401395872, 21275613503385328981848681986

Offset: 0

Author

Seiichi Manyama, Oct 31 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A377548.

Cf. A364985.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x))^2)/x))

PARI

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

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364985.

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