A367423 Expansion of e.g.f. 1 / sqrt(1 + log(1 - 2*x)).

1, 1, 5, 41, 465, 6729, 118437, 2455809, 58630401, 1584058161, 47783202213, 1591924168185, 58055219617425, 2300356943749305, 98409722434170885, 4520749198158270225, 221954573405993807745, 11598560660172502840545, 642753897983638032821445

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (1 - 1/2 * k/n) * (k-1)! * binomial(n,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 2*j+1)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A097397, A352117.

Sequence in context: A096364 A210661 A049119 * A332236 A305981 A032188

Adjacent sequences: A367420 A367421 A367422 * A367424 A367425 A367426

Keyword

nonn

Author

Seiichi Manyama, Nov 18 2023

Status

approved