A386509 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^6 * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 3, 583, 1702357, 34872788861, 3269533221246901, 1067826281292319819285, 1005038096045094314876257929, 2371191405228277266497568590592937, 12601507027818562471139233302156639660841, 138616715922712004054565802733773706346507326441

Offset: 0

Author

Seiichi Manyama, Jul 24 2025

Keywords

• nonn

Crossrefs

Cf. A143925, A386505, A386506, A386507, A386508.

Cf. A385943, A386447.

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).