A245051 Number of hybrid 8-ary trees with n internal nodes.

1, 2, 31, 691, 18054, 515892, 15615159, 492007235, 15968172965, 530169356965, 17922457144129, 614796956579459, 21346411113410148, 748762981653051898, 26493592534823331169, 944491728494004127029, 33892155096781949014406, 1223212951343094980654244

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/(7*n+1) * Sum_{i=0..n} C(7*n+i,i)*C(7*n+i+1,n-i).

a(n) = [x^n] ((1+x)/(1-x-x^2))^(7*n+1) / (7*n+1).

G.f. satisfies: A(x) = (1+x*A(x)^7) * (1+x*A(x)^8).

Maple

a:= n-> add(binomial(7*n+i, i)*binomial(7*n+i+1, n-i), i=0..n)/(7*n+1):
seq(a(n), n=0..20);

Crossrefs

Column k=8 of A245049.

Sequence in context: A362860 A057692 A058244 * A024235 A010789 A333349

Adjacent sequences: A245048 A245049 A245050 * A245052 A245053 A245054

Keyword

nonn

Author

Alois P. Heinz, Jul 10 2014

Status

approved