A386454 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} binomial(k+3,4) * a(k) * a(n-1-k).

1, 1, 2, 13, 220, 8148, 586948, 75141039, 15930666825, 5289069956220, 2628685323745449, 1884772989271329869, 1890430039448133854031, 2584219798288871040676608, 4708450397910844142927823544, 11215531466814325127916787062534, 34341962107081618846057340207455738

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386452, A386453, A386455.

Cf. A385876.

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+3, 4)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..4} binomial(3,k-1) * x^k/k! * (d^k/dx^k A(x)) ).