A245054 Number of hybrid (n+1)-ary trees with n internal nodes.

1, 2, 11, 155, 3920, 148348, 7585749, 492007235, 38798085127, 3609589528430, 387451906370509, 47166300422957938, 6423902286587614629, 968148639856266236900, 159999832729471473179245, 28775750341340155354161817, 5595702924360902427922341048

Offset: 0

Author

Alois P. Heinz, Jul 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• SeoungJi Hong and SeungKyung Park, Hybrid d-ary trees and their generalization, Bull. Korean Math. Soc. 51 (2014), No. 1, pp. 229-235

Crossrefs

Main diagonal of A245049.

Programs

Maple

a:= n-> add(binomial(n^2+i, i)*binomial(n^2+i+1, n-i), i=0..n)/(n^2+1):
seq(a(n), n=0..20);

Mathematica

Table[Sum[Binomial[n^2+i,i]*Binomial[n^2+i+1, n-i], {i,0,n}]/(n^2+1),{n,0,20}] (* Vaclav Kotesovec, Jul 11 2014 *)

Formula

a(n) = 1/(n^2+1) * Sum_{i=0..n} C(n^2+i,i) * C(n^2+i+1,n-i).

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

a(n) = A245049(n,n+1).

a(n) ~ 2^(n-1/2) * exp(n+1/4) * n^(n-5/2) / sqrt(Pi). - Vaclav Kotesovec, Jul 11 2014