A386447 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^6 * a(k) * a(n-1-k).

1, 1, 2, 131, 95760, 392424606, 6132419429842, 286126426174265119, 33663060172069656177612, 8824636572155130972996888814, 4689791333849576329442118802082252, 4689800713441077274969296364554337253614, 8308277421310507219950890075481144453543272228

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386443, A386444, A386445, A386446.

Cf. A385834.

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, j^6*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).