A385939 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^2) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 5, 88, 3893, 352536, 57322537, 15277686880, 6239711818377, 3708478187297920, 3079046917046731661, 3455392385954013825024, 5100835934217411940938685, 9682263835381845999967986688, 23180826149963609282826172967025, 68850271609123855250628849758027776

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A156326, A385940, A385941, A385942, A385943.

Cf. A385830.

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, (1+j)*(1+j^2)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) + x^2 * (d/dx A(x)) + x^3 * (d^2/dx^2 A(x)) ).