A376346 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^3)) ).

1, 0, 0, 0, 24, 0, 0, 2520, 201600, 0, 1209600, 259459200, 16765056000, 1556755200, 639307468800, 100037089152000, 5967179676057600, 2815858805760000, 784290778951680000, 107737010595422208000, 6175610876944244736000, 8813187524619878400000, 2070195245189633802240000, 264886226510800191897600000

Offset: 0

Author

Seiichi Manyama, Sep 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A376344.

Cf. A375562.

Programs

PARI

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

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (2*n-3*k)! * |Stirling1(k,n-3*k)|/k!.