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

0,2

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/(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).

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);

Crossrefs

Column k=10 of A245049.

Sequence in context: A319520 A209632 A266863 * A352021 A177773 A274574

Adjacent sequences: A245050 A245051 A245052 * A245054 A245055 A245056

Keyword

nonn

Author

Alois P. Heinz, Jul 10 2014

Status

approved