A376347 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^3) - 1)) ).

1, 0, 0, 0, 24, 0, 0, 2520, 201600, 0, 604800, 259459200, 16765056000, 259459200, 406832025600, 100037089152000, 5963169474662400, 844757641728000, 560207699251200000, 107716905363549081600, 6157546579533533184000, 3525275009847951360000, 1582967914636148232192000, 264668100119565849907200000

Offset: 0

Author

Seiichi Manyama, Sep 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370988, A376345.

Cf. A370928, A375589.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^3)-1)))/x))

PARI

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

Formula

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