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

0,2

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

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).

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);

Crossrefs

Column k=9 of A245049.

Sequence in context: A279734 A277294 A191807 * A266316 A110697 A322514

Adjacent sequences: A245049 A245050 A245051 * A245053 A245054 A245055

Keyword

nonn

Author

Alois P. Heinz, Jul 10 2014

Status

approved