A381568 G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^2.

1, 2, 5, 22, 126, 884, 7149, 64688, 641836, 6888740, 79203860, 968503090, 12525131474, 170555767116, 2436592516874, 36409825487380, 567612675812796, 9211031425896752, 155283809480528788, 2714788300934206360, 49140787009610861896, 919625415852055598804, 17768937720619971300781

Offset: 0

Author

Seiichi Manyama, Feb 28 2025

Keywords

• nonn

Crossrefs

Column k=1 of A381567.

Cf. A087949, A120970, A143508, A381570.

Programs

PARI

a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-2*j+2*k, j)/(n-j+k)*a(n-j, j)));

Formula

See A381567.

G.f.: B(x)^2, where B(x) is the g.f. of A143508.