A375806 Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^2.

1, 2, 6, 30, 192, 1520, 14220, 153720, 1881600, 25728192, 388402560, 6415960320, 115078138560, 2227056923520, 46247253212160, 1025696098627200, 24195406204569600, 604862279807385600, 15973029429800002560, 444299711254300661760, 12983645995613669376000

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A375798, A375807.

Cf. A375680.

Programs

PARI

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

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375798.

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