A245054 - OEIS

%I #11 Sep 08 2018 17:18:41

%S 1,2,11,155,3920,148348,7585749,492007235,38798085127,3609589528430,

%T 387451906370509,47166300422957938,6423902286587614629,

%U 968148639856266236900,159999832729471473179245,28775750341340155354161817,5595702924360902427922341048

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

%H Alois P. Heinz, <a href="/A245054/b245054.txt">Table of n, a(n) for n = 0..200</a>

%H SeoungJi Hong and SeungKyung Park, <a href="http://dx.doi.org/10.4134/BKMS.2014.51.1.229">Hybrid d-ary trees and their generalization</a>, Bull. Korean Math. Soc. 51 (2014), No. 1, pp. 229-235

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

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

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

%F a(n) ~ 2^(n-1/2) * exp(n+1/4) * n^(n-5/2) / sqrt(Pi). - _Vaclav Kotesovec_, Jul 11 2014

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

%p seq(a(n), n=0..20);

%t 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 *)

%Y Main diagonal of A245049.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jul 10 2014