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 A137956 #11 Nov 22 2017 05:25:57
%S A137956 1,1,4,14,64,301,1500,7738,40948,221278,1215284,6765148,38083556,
%T A137956 216431253,1240048740,7155236960,41542685352,242513393884,
%U A137956 1422608044604,8381507029660,49574494112992,294260899150492,1752288415205896
%N A137956 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^2)^4.
%H A137956 G. C. Greubel, <a href="/A137956/b137956.txt">Table of n, a(n) for n = 0..1000</a>
%H A137956 Vaclav Kotesovec, <a href="/A137956/a137956.txt">Recurrence</a>
%F A137956 G.f.: A(x) = 1 + x*B(x)^4 where B(x) is the g.f. of A137955.
%F A137956 a(n) = Sum_{k=0..n-1} C(4*(n-k),k)/(n-k) * C(2*k,n-k-1) for n>0 with a(0)=1. - _Paul D. Hanna_, Jun 16 2009
%F A137956 a(n) ~ sqrt(4*s*(1-s)*(2-3*s) / ((28*s - 16)*Pi)) / (n^(3/2) * r^n), where r = 0.1569043698639381952962655091205241634381480571697... and s = 1.683635070625292013962854364673077567156937629734... are real roots of the system of equations s = 1 + r*(1 + r*s^2)^4, 8 * r^2 * s * (1 + r*s^2)^3 = 1. - _Vaclav Kotesovec_, Nov 22 2017
%t A137956 Flatten[{1,Table[Sum[Binomial[4*(n-k),k]/(n-k)*Binomial[2*k,n-k-1],{k,0,n-1}],{n,1,20}]}] (* _Vaclav Kotesovec_, Sep 18 2013 *)
%o A137956 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*(1+x*A^2)^4);polcoeff(A,n)}
%o A137956 (PARI) a(n)=if(n==0,1,sum(k=0,n-1,binomial(4*(n-k),k)/(n-k)*binomial(2*k,n-k-1))) \\ _Paul D. Hanna_, Jun 16 2009
%Y A137956 Cf. A137955, A137957; A137958, A137964, A137971.
%K A137956 nonn
%O A137956 0,3
%A A137956 _Paul D. Hanna_, Feb 26 2008