A385836 a(n) = 1 + Sum_{k=0..n-1} (1 + k^3) * a(k) * a(n-1-k).

1, 2, 7, 79, 2446, 166618, 21508712, 4732995201, 1642479584974, 847546182102241, 621260202463120771, 623749689526374747439, 832709044623310548285995, 1442255257225526024262579955, 3174408056872712362090099214740, 8723280646832436679639469748539639

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A321087, A385835, A385837, A385838, A385839.

Cf. A385759.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+j^3)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*A(x) - x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ) ).