A245052 Number of hybrid 9-ary trees with n internal nodes.

1, 2, 35, 885, 26264, 852909, 29347189, 1051325430, 38798085127, 1464834251301, 56313293080748, 2196846557946047, 86747889084025665, 3460614563468144968, 139261626165295942419, 5646457490910228197571, 230445856010164690649448, 9459481451214159977362615

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=9 of A245049.

Programs

Maple

a:= n-> add(binomial(8*n+i, i)*binomial(8*n+i+1, n-i), i=0..n)/(8*n+1):
seq(a(n), n=0..20);

Formula

a(n) = 1/(8*n+1) * Sum_{i=0..n} C(8*n+i,i)*C(8*n+i+1,n-i).

a(n) = [x^n] ((1+x)/(1-x-x^2))^(8*n+1) / (8*n+1).

G.f. satisfies: A(x) = (1+x*A(x)^8) * (1+x*A(x)^9).