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 A188455 #11 Mar 30 2012 18:37:26 %S A188455 1,1,5,77,3191,332481,83495679,49089025473,66142622730623, %T A188455 200954040909283841,1359156203343916471295,20253823024219712679748609, %U A188455 659335186924510858208484730879,46554554840488755704034417937268737 %N A188455 G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1 + 2^n*x)^(2n+1). %C A188455 G.f. satisfies a variant of an identity of the Catalan numbers (A000108): %C A188455 1 = Sum_{n>=0} A000108(n)*x^n/(1 + x)^(2n+1). %C A188455 Also, g.f. satisfies a variant of an identity involving A003024: %C A188455 1 = Sum_{n>=0} A003024(n)*x^n/(1 + 2^n*x)^(n+1), %C A188455 where A003024(n) is the number of acyclic digraphs with n labeled nodes. %e A188455 G.f.: 1 = 1/(1+x) + x/(1+2*x)^3 + 5*x^2/(1+4*x)^5 + 77*x^3/(1+8*x)^7 + 3191*x^4/(1+16*x)^9 + 332481*x^5/(1+32*x)^11 +... %o A188455 (PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k/(1+2^k*x+x*O(x^n))^(2*k+1)), n)} %Y A188455 Cf. A188456, A188457, A003024. %K A188455 nonn %O A188455 0,3 %A A188455 _Paul D. Hanna_, Mar 31 2011