A353880 Expansion of e.g.f. 1/(1 - (x * log(1-x))^2 / 4).

1, 0, 0, 0, 6, 30, 165, 1050, 10192, 108864, 1230660, 14758920, 195861996, 2852815680, 44880446520, 753211040400, 13458760362720, 255688784416800, 5149255813778160, 109489194918180000, 2450182706364430080, 57567025900160259840, 1417073899136197468320

Offset: 0

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A052830, A353881, A353882.

Cf. A346921, A353883.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*log(1-x))^2/4)))

PARI

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * |Stirling1(n-2*k,2*k)|/(4^k * (n-2*k)!).