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

0,2

Links

Table of n, a(n) for n=0..22.

Formula

See A381567.

Prog

(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)));

Crossrefs

Column k=1 of A381567.

Cf. A087949, A120970, A381570.

Sequence in context: A066305 A020093 A329260 * A111542 A342432 A246542

Adjacent sequences: A381565 A381566 A381567 * A381569 A381570 A381571

Keyword

nonn,new

Author

Seiichi Manyama, Feb 28 2025

Status

approved