A245052 - OEIS

%I #6 Jul 10 2014 19:16:59

%S 1,2,35,885,26264,852909,29347189,1051325430,38798085127,

%T 1464834251301,56313293080748,2196846557946047,86747889084025665,

%U 3460614563468144968,139261626165295942419,5646457490910228197571,230445856010164690649448,9459481451214159977362615

%N Number of hybrid 9-ary trees with n internal nodes.

%H Alois P. Heinz, <a href="/A245052/b245052.txt">Table of n, a(n) for n = 0..300</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/(8*n+1) * Sum_{i=0..n} C(8*n+i,i)*C(8*n+i+1,n-i).

%F a(n) = [x^n] ((1+x)/(1-x-x^2))^(8*n+1) / (8*n+1).

%F G.f. satisfies: A(x) = (1+x*A(x)^8) * (1+x*A(x)^9).

%p a:= n-> add(binomial(8*n+i, i)*binomial(8*n+i+1, n-i), i=0..n)/(8*n+1):

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

%Y Column k=9 of A245049.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jul 10 2014