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 A137955 #12 Nov 22 2017 05:24:53
%S A137955 1,1,2,9,36,172,842,4310,22676,121896,666884,3699973,20771096,
%T A137955 117765084,673367034,3878538930,22483446152,131070712924,767929882240,
%U A137955 4519387797894,26704456819984,158367557278412,942285096541344,5623496055739052,33653373190735484
%N A137955 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^4)^2.
%H A137955 G. C. Greubel, <a href="/A137955/b137955.txt">Table of n, a(n) for n = 0..1000</a>
%H A137955 Vaclav Kotesovec, <a href="/A137955/a137955.txt">Recurrence</a>
%F A137955 G.f.: A(x) = 1 + x*B(x)^2 where B(x) is the g.f. of A137956.
%F A137955 a(n) = Sum_{k=0..n-1} C(2*(n-k),k)/(n-k) * C(4*k,n-k-1) for n>0 with a(0)=1. - _Paul D. Hanna_, Jun 16 2009
%F A137955 a(n) ~ sqrt(2*s*(1-s)*(4-5*s) / ((56*s - 48)*Pi)) / (n^(3/2) * r^n), where r = 0.1569043698639381952962655091205241634381480571697... and s = 1.444765371242615455251538467189577278901629278244... are real roots of the system of equations s = 1 + r*(1 + r*s^4)^2, 8 * r^2 * s^3 * (1 + r*s^4) = 1. - _Vaclav Kotesovec_, Nov 22 2017
%t A137955 Flatten[{1,Table[Sum[Binomial[2*(n-k),k]/(n-k)*Binomial[4*k,n-k-1],{k,0,n-1}],{n,1,20}]}] (* _Vaclav Kotesovec_, Sep 18 2013 *)
%o A137955 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*(1+x*A^4)^2);polcoeff(A,n)}
%o A137955 (PARI) a(n)=if(n==0,1,sum(k=0,n-1,binomial(2*(n-k),k)/(n-k)*binomial(4*k,n-k-1))) \\ _Paul D. Hanna_, Jun 16 2009
%Y A137955 Cf. A137956, A137954; A137952, A137960, A137967.
%K A137955 nonn
%O A137955 0,3
%A A137955 _Paul D. Hanna_, Feb 26 2008