A385955 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+6,6) * a(k) * a(n-1-k).

1, 1, 8, 239, 20595, 4369086, 2027570077, 1877595433603, 3225737601183428, 9693366952072675847, 48534731177400280613882, 388763324236561973987746008, 4812113062706722698140922709260, 89341696197620005494613697916344217, 2424197647354438894347947373843634554628

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A351798, A385952, A385953, A385954.

Cf. A385948.

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

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - Sum_{k=0..6} binomial(6,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.