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 A137963 #10 Mar 03 2018 13:52:56
%S A137963 1,1,5,25,160,1075,7671,56760,431865,3357790,26558520,213032988,
%T A137963 1728808700,14168337265,117096909495,974842628790,8167462511193,
%U A137963 68813778610350,582675107162175,4955767502292960,42318868510894860
%N A137963 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^5.
%H A137963 Vaclav Kotesovec, <a href="/A137963/b137963.txt">Table of n, a(n) for n = 0..350</a>
%F A137963 G.f.: A(x) = 1 + x*B(x)^5 where B(x) is the g.f. of A137962.
%F A137963 a(n) = Sum_{k=0..n-1} C(5*(n-k),k)/(n-k) * C(3*k,n-k-1) for n>0 with a(0)=1. - _Paul D. Hanna_, Jun 16 2009
%F A137963 a(n) ~ sqrt(5*s*(1-s)*(3-4*s) / ((84*s - 60)*Pi)) / (n^(3/2) * r^n), where r = 0.1085884782751570249717333800652227343328635496829... and s = 1.404764002126311415321709718173984955120001713401... are real roots of the system of equations s = 1 + r*(1 + r*s^3)^5, 15 * r^2 * s^2 * (1 + r*s^3)^4 = 1. - _Vaclav Kotesovec_, Nov 22 2017
%o A137963 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*(1+x*A^3)^5);polcoeff(A,n)}
%o A137963 (PARI) a(n)=if(n==0,1,sum(k=0,n-1,binomial(5*(n-k),k)/(n-k)*binomial(3*k,n-k-1))) \\ _Paul D. Hanna_, Jun 16 2009
%Y A137963 Cf. A137962, A137964; A137961, A137965, A137973.
%K A137963 nonn
%O A137963 0,3
%A A137963 _Paul D. Hanna_, Feb 26 2008