A245053 Number of hybrid 10-ary trees with n internal nodes.

1, 2, 39, 1103, 36650, 1333156, 51392991, 2062946770, 85311756697, 3609589528430, 155513170273468, 6799151325525095, 300899538364069838, 13453346159391591392, 606776046327452415295, 27573839101542183831805, 1261298294289947726165466, 58029238642196850552991302

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=10 of A245049.

Programs

Maple

a:= n-> add(binomial(9*n+i, i)*binomial(9*n+i+1, n-i), i=0..n)/(9*n+1):
seq(a(n), n=0..20);

Formula

a(n) = 1/(9*n+1) * Sum_{i=0..n} C(9*n+i,i)*C(9*n+i+1,n-i).

a(n) = [x^n] ((1+x)/(1-x-x^2))^(9*n+1) / (9*n+1).

G.f. satisfies: A(x) = (1+x*A(x)^9) * (1+x*A(x)^10).