A386452 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} binomial(k+1,2) * a(k) * a(n-1-k).

1, 1, 2, 9, 71, 856, 14639, 338086, 10167592, 386920264, 18200571057, 1037970049307, 70605576249333, 5649723531576365, 525507834721871564, 56235831305760575845, 6861362229615344431713, 946930149578851143467375, 146781656943702604491445861, 25394248429778915431816805711

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386453, A386454, A386455.

Cf. A385874.

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, binomial(j+1, 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^3/2 * (d^2/dx^2 A(x)) ).