A245053 - OEIS

%I #6 Jul 10 2014 19:18:05

%S 1,2,39,1103,36650,1333156,51392991,2062946770,85311756697,

%T 3609589528430,155513170273468,6799151325525095,300899538364069838,

%U 13453346159391591392,606776046327452415295,27573839101542183831805,1261298294289947726165466,58029238642196850552991302

%N Number of hybrid 10-ary trees with n internal nodes.

%H Alois P. Heinz, <a href="/A245053/b245053.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/(9*n+1) * Sum_{i=0..n} C(9*n+i,i)*C(9*n+i+1,n-i).

%F a(n) = [x^n] ((1+x)/(1-x-x^2))^(9*n+1) / (9*n+1).

%F G.f. satisfies: A(x) = (1+x*A(x)^9) * (1+x*A(x)^10).

%p a:= n-> add(binomial(9*n+i, i)*binomial(9*n+i+1, n-i), i=0..n)/(9*n+1):

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

%Y Column k=10 of A245049.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jul 10 2014