A376391 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(2 - exp(x))^3 ) )^(2/3).

1, 2, 20, 386, 11252, 441722, 21867764, 1308580226, 91904288420, 7413237414602, 675503178005108, 68631619821747842, 7693344955213551428, 943236099444038389082, 125565496331888560573172, 18037220418654308659836674, 2780985275750966018759898212, 458079154394191702424821932842

Offset: 0

Author

Seiichi Manyama, Sep 22 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A367135, A376390.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(2-exp(x))^3)/x)^(2/3)))

PARI

a(n) = 2*sum(k=0, n, (3*n+k+1)!*stirling(n, k, 2))/(3*n+2)!;

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367135.

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