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

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=7 of A245049.

Programs

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);

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).