A385837 a(n) = 1 + Sum_{k=0..n-1} (1 + k^4) * a(k) * a(n-1-k).

1, 2, 7, 135, 11472, 2983290, 1876558882, 2439543938823, 5867113337771476, 24055177364999767957, 157922269330003687462469, 1579854504025376907525660119, 23136970006572094830720177877037, 479860765871358769352536441406761329, 13707222893156109310485886790873337444816

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A321087, A385835, A385836, A385838, A385839.

Cf. A385760.

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^4)*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..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ) ).