A376350 E.g.f. satisfies A(x) = 1/(1 - x^2*A(x)^2)^(x*A(x)).

1, 0, 0, 6, 0, 60, 2520, 1680, 181440, 6138720, 18295200, 1444988160, 46443196800, 357015859200, 25016537145600, 818965321574400, 12259854032025600, 815066633667686400, 28461465853402982400, 691667282863484928000, 45198900807076912896000, 1739192274792359202816000, 60318174486002275287244800

Offset: 0

Author

Seiichi Manyama, Sep 21 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A001761, A184949, A371147.

Cf. A353226.

Programs

PARI

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

PARI

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

Formula

E.g.f.: (1/x) * Series_Reversion( x*(1 - x^2)^x ).

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