A385947 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+5,5) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 7, 166, 10029, 1321025, 341733205, 160453080950, 128422430092385, 166469443066352440, 334968718604910165425, 1009644894131844004090200, 4422360688027934597152329025, 27423466157672001507611296316100, 235350249980804930971638499216115775

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A000272, A156325, A385945, A385946, A385948.

Cf. A385954.

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

Formula

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