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%I #6 Jul 10 2014 19:15:01
%S 1,2,27,521,11764,290305,7585749,206294771,5778015219,165541098701,
%T 4828687088591,142916854642246,4281359716909135,129567073833995237,
%U 3955263087052174005,121649279851846182073,3766009580469162813492,117260083892211493754415
%N Number of hybrid 7-ary trees with n internal nodes.
%H Alois P. Heinz, <a href="/A245050/b245050.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/(6*n+1) * Sum_{i=0..n} C(6*n+i,i)*C(6*n+i+1,n-i).
%F a(n) = [x^n] ((1+x)/(1-x-x^2))^(6*n+1) / (6*n+1).
%F G.f. satisfies: A(x) = (1+x*A(x)^6) * (1+x*A(x)^7).
%p a:= n-> add(binomial(6*n+i, i)*binomial(6*n+i+1, n-i), i=0..n)/(6*n+1):
%p seq(a(n), n=0..20);
%Y Column k=7 of A245049.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Jul 10 2014
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