A386443 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^2 * a(k) * a(n-1-k).

1, 1, 2, 11, 120, 2166, 58642, 2231959, 113926332, 7522541374, 624529876412, 63711767096254, 7837308575551868, 1144321503810951264, 195687862794184808186, 38747465910056072904383, 8795888226933223095245628, 2269380895962602685279019270, 660399219910352767447886420340

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386444, A386445, A386446, A386447.

Cf. A385830, A386448, A386452.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, j^2*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x^2 * (d/dx A(x)) - x^3 * (d^2/dx^2 A(x)) ).