This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A239109 #24 Oct 02 2019 07:27:15
%S A239109 1,2,23,375,7138,148348,3262975,74673216,1759690865,42412172598,
%T A239109 1040644972314,25907046248766,652763779424538,16614703783094140,
%U A239109 426563932954831827,11033640140115676862,287265076610919864178,7522060666571155198520,197969862318742854908470
%N A239109 Number of hybrid 6-ary trees with n internal nodes.
%H A239109 Alois P. Heinz, <a href="/A239109/b239109.txt">Table of n, a(n) for n = 0..300</a>
%H A239109 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. See p. 233.
%F A239109 From _Paul D. Hanna_, Mar 30 2014: (Start)
%F A239109 G.f. A(x) satisfies:
%F A239109 (1) A(x) = (1 + x*A(x)^5) * (1 + x*A(x)^6).
%F A239109 (2) A(x) = ( (1/x)*Series_Reversion( x*(1-x-x^2)^5/(1+x)^5 ) )^(1/5).
%F A239109 (3) A(x) = exp( Sum_{n>=1} x^n*A(x)^(4*n)/n * Sum_{k=0..n} C(n,k)^2 * A(x)^k ).
%F A239109 (4) A(x) = exp( Sum_{n>=1} x^n*A(x)^(5*n)/n * Sum_{k=0..n} C(n,k)^2 / A(x)^k ).
%F A239109 (5) A(x) = Sum_{n>=0} Fibonacci(n+2) * x^n * A(x)^(5*n).
%F A239109 (6) A(x) = G(x*A(x)^4) where G(x) = A(x/G(x)^4) is the g.f. of A007863 (number of hybrid binary trees with n internal nodes).
%F A239109 The formal inverse of g.f. A(x) is (sqrt(1-2*x+5*x^2) - (1+x))/(2*x^6).
%F A239109 a(n) = [x^n] ( (1+x)/(1-x-x^2) )^(5*n+1) / (5*n+1).
%F A239109 (End)
%t A239109 (1/x InverseSeries[x*(1 - x - x^2)^5/(1 + x)^5 + O[x]^20])^(1/5) // CoefficientList[#, x]& (* _Jean-François Alcover_, Oct 02 2019 *)
%o A239109 (PARI) a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=(1 + x*A^5)*(1 + x*A^6)); polcoeff(A, n)
%o A239109 for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Mar 30 2014
%o A239109 (PARI) a(n)=polcoeff( ((1/x)*serreverse( x*(1-x-x^2)^5/(1+x +x*O(x^n))^5))^(1/5), n)
%o A239109 for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Mar 30 2014
%o A239109 (PARI) a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^2*A^j)*x^m*A^(4*m)/m))); polcoeff(A, n)
%o A239109 for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Mar 30 2014
%o A239109 (PARI) a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^2/A^j)*x^m*A^(5*m)/m))); polcoeff(A, n)
%o A239109 for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Mar 30 2014
%o A239109 (PARI) a(n)=polcoeff(((1+x)/(1-x-x^2 +x*O(x^n)))^(5*n+1)/(5*n+1), n)
%o A239109 for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Mar 30 2014
%Y A239109 Cf. A000045, A007863, A215654, A239107, A239108, A239109.
%Y A239109 Column k=6 of A245049.
%K A239109 nonn
%O A239109 0,2
%A A239109 _N. J. A. Sloane_, Mar 26 2014