A385877 a(n) = 1 + Sum_{k=0..n-1} binomial(k+4,5) * a(k) * a(n-1-k).

1, 1, 2, 14, 309, 17637, 2240632, 566921596, 262489646519, 208155482551991, 268104800528280951, 537014337938584568385, 1613191612128443060280697, 7048035233444754041436840277, 43620293298146615746333469478901, 373782307403691698916363133787269075

Offset: 0

Author

Seiichi Manyama, Jul 11 2025

Keywords

• nonn

Crossrefs

Cf. A143917, A385874, A385875, A385876.

Cf. A385843.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, binomial(j+4, 5)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..5} binomial(4,k-1) * x^k/k! * (d^k/dx^k A(x)) ) ).