A385838 a(n) = 1 + Sum_{k=0..n-1} (1 + k^5) * a(k) * a(n-1-k).

1, 2, 7, 247, 61006, 62715298, 196236522104, 1526720482525833, 25665699044532909262, 841116296816234980686001, 49670440804927429155777517363, 4967242766473223753247263215133503, 799999284003076533259467892632499306811, 199068621859048073152067295737349123675521467

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A321087, A385835, A385836, A385837, A385839.

Cf. A385761, A385843.

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^5)*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..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ) ).