A381029 G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^2)^2).

1, 1, 3, 16, 113, 955, 9178, 97427, 1121705, 13836694, 181295019, 2507119320, 36416096984, 553461581406, 8774534872463, 144744539399484, 2479088917439527, 44004108702467428, 808171916050540308, 15335535608825061803, 300272362335527090277, 6059534345675248667550

Offset: 0

Author

Seiichi Manyama, Mar 01 2025

Keywords

• nonn

Crossrefs

Cf. A088714, A381615.

Cf. A120971, A143508, A381600.

Cf. A381572.

Programs

PARI

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

Formula

Let a(n,k) = [x^n] A(x)^k.

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