A376344 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2)) ).

1, 0, 0, 6, 0, 60, 2880, 1680, 201600, 8074080, 19958400, 1824197760, 69854400000, 436929292800, 36099561738240, 1392369634656000, 17026966410854400, 1344523178718720000, 54023115000830976000, 1095484919871908966400, 84994409643640713216000, 3650011125774294048768000, 109122812080533877712486400

Offset: 0

Author

Seiichi Manyama, Sep 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370993, A376346.

Cf. A370994, A375561.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2)))/x))

PARI

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

Formula

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