A354389 Expansion of e.g.f. 1/(1 + log(1 + x)^2 / 2).

1, 0, -1, 3, -5, -10, 146, -756, 1086, 23400, -300066, 1855590, 341826, -165915828, 2158958556, -10006622640, -172337345496, 4941605486016, -64365944851512, 339328464492456, 5510899593823176, -157099566384759600, 1059259019507498160, 41957473280879898720

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling1(k,2) * a(n-k).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1+x)^2/2)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i, j)*stirling(j, 2, 1)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\2, (2*k)!*stirling(n, 2*k, 1)/(-2)^k);

Crossrefs

Cf. A346921, A354317, A354390, A354391.

Sequence in context: A305510 A024329 A354517 * A297422 A064523 A365443

Adjacent sequences: A354386 A354387 A354388 * A354390 A354391 A354392

Keyword

sign

Author

Seiichi Manyama, May 25 2022

Status

approved