A376293 E.g.f. satisfies A(x) = 1 + (x*A(x))^3 * (exp(x*A(x)) - 1).

1, 0, 0, 0, 24, 60, 120, 210, 161616, 1633464, 10584720, 54886590, 10785520680, 243865703796, 3309354530664, 34340235932730, 3229131046905120, 123251776925401200, 2846181122195004576, 49221175229381943414, 3060186440577720774840

Offset: 0

Author

Seiichi Manyama, Sep 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A000272, A371119, A371139.

Programs

PARI

a(n) = n!^2*sum(k=0, n\4, stirling(n-3*k, k, 2)/((n-3*k)!*(n-k+1)!));

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/4)} Stirling2(n-3*k,k)/( (n-3*k)! * (n-k+1)! ).

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