A385874 a(n) = 1 + Sum_{k=0..n-1} binomial(k+1,2) * a(k) * a(n-1-k).

1, 1, 2, 8, 57, 639, 10357, 229588, 6686619, 248013315, 11425386222, 640413284553, 42933889931191, 3393203732253145, 312268381507616935, 33107736233111305459, 4006699123399932333697, 548987463226205098599755, 84552444466155546810368421, 14544161652321384236939516147

Offset: 0

Author

Seiichi Manyama, Jul 11 2025

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..270

Crossrefs

Cf. A143917, A385875, A385876, A385877.

Cf. A385830, A385835, A385840.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+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) * ( 1 - x^2 * (d/dx A(x)) - x^3/2 * (d^2/dx^2 A(x)) ) ).