A385953 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+4,4) * a(k) * a(n-1-k).

1, 1, 6, 101, 3756, 271256, 34761512, 7372486163, 2448035959989, 1216747945481685, 872431867857009866, 875060598719254613963, 1196215918953589596769516, 2179513438308809548333358500, 5191611931593198935913809439220, 15896735560092998091331427433546666

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A351798, A385952, A385954, A385955.

Cf. A385946.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, binomial(j+4, 4)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - Sum_{k=0..4} binomial(4,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.