A386455 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} binomial(k+4,5) * a(k) * a(n-1-k).

1, 1, 2, 15, 344, 19962, 2555592, 649147331, 301207446317, 239159429472132, 308276821981867349, 617786997525975886618, 1856450241316927094671750, 8112688179283378712969957414, 50217541700003149682333160103969, 430364340522944093019900101527085125

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386452, A386453, A386454.

Cf. A385877.

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+4, 5)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..5} binomial(4,k-1) * x^k/k! * (d^k/dx^k A(x)) ).