A371122 E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)).

1, 0, 2, 3, 104, 570, 19284, 220500, 7975008, 148889664, 5911249680, 157016471040, 6913129099392, 239681708117280, 11734594390915200, 501510627153244800, 27265653826293749760, 1380895751066249779200, 83060557136719693406208

Offset: 0

Author

Seiichi Manyama, Mar 11 2024

Keywords

• nonn

Crossrefs

Cf. A370993, A371117, A371121.

Cf. A371120.

Programs

PARI

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n+2*k)! * |Stirling1(n-k,k)|/( (n-k)! * (n+k+1)! ).