A375687 Expansion of e.g.f. 1 / sqrt(1 + 2 * x * log(1 - x)).

1, 0, 2, 3, 44, 210, 2934, 26040, 404592, 5302584, 95029560, 1632252600, 33865401096, 712672337520, 16986980278800, 420485947572600, 11386595338156800, 322890555922925760, 9820815078397642560, 313247186941438569600, 10588974153880701225600

Offset: 0

Author

Seiichi Manyama, Aug 24 2024

Keywords

• nonn

Crossrefs

Cf. A001147, A052830, A346978, A367878.

Programs

PARI

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

PARI

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

Formula

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