A245051 Number of hybrid 8-ary trees with n internal nodes.

1, 2, 31, 691, 18054, 515892, 15615159, 492007235, 15968172965, 530169356965, 17922457144129, 614796956579459, 21346411113410148, 748762981653051898, 26493592534823331169, 944491728494004127029, 33892155096781949014406, 1223212951343094980654244

Offset: 0

Author

Alois P. Heinz, Jul 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• SeoungJi Hong and SeungKyung Park, Hybrid d-ary trees and their generalization, Bull. Korean Math. Soc. 51 (2014), No. 1, pp. 229-235

Crossrefs

Column k=8 of A245049.

Programs

Maple

a:= n-> add(binomial(7*n+i, i)*binomial(7*n+i+1, n-i), i=0..n)/(7*n+1):
seq(a(n), n=0..20);

Formula

a(n) = 1/(7*n+1) * Sum_{i=0..n} C(7*n+i,i)*C(7*n+i+1,n-i).

a(n) = [x^n] ((1+x)/(1-x-x^2))^(7*n+1) / (7*n+1).

G.f. satisfies: A(x) = (1+x*A(x)^7) * (1+x*A(x)^8).