A245050 Number of hybrid 7-ary trees with n internal nodes.

1, 2, 27, 521, 11764, 290305, 7585749, 206294771, 5778015219, 165541098701, 4828687088591, 142916854642246, 4281359716909135, 129567073833995237, 3955263087052174005, 121649279851846182073, 3766009580469162813492, 117260083892211493754415

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/(6*n+1) * Sum_{i=0..n} C(6*n+i,i)*C(6*n+i+1,n-i).

a(n) = [x^n] ((1+x)/(1-x-x^2))^(6*n+1) / (6*n+1).

G.f. satisfies: A(x) = (1+x*A(x)^6) * (1+x*A(x)^7).

Maple

a:= n-> add(binomial(6*n+i, i)*binomial(6*n+i+1, n-i), i=0..n)/(6*n+1):
seq(a(n), n=0..20);

Crossrefs

Column k=7 of A245049.

Sequence in context: A363961 A240701 A240638 * A242009 A121137 A203429

Adjacent sequences: A245047 A245048 A245049 * A245051 A245052 A245053

Keyword

nonn

Author

Alois P. Heinz, Jul 10 2014

Status

approved