A375698 Expansion of e.g.f. 1 / sqrt(1 + x^2 * log(1 - x)).

1, 0, 0, 3, 6, 20, 360, 2394, 17220, 252720, 2963520, 34525260, 552027960, 8860952880, 142907532768, 2682870913800, 53297669552400, 1086135012144000, 24087251436249600, 566843973576536880, 13834256829134364000, 357412359616922433600, 9723652519748883408000

Offset: 0

Author

Seiichi Manyama, Aug 25 2024

Keywords

• nonn

Crossrefs

Cf. A001147, A351503, A351505, A375715.

Programs

PARI

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

PARI

a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = n!*sum(k=0, n\3, a001147(k)*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} A001147(k) * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).