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 A188456 #18 Dec 09 2017 11:15:23
%S A188456 1,1,4,44,1216,80640,12460032,4393091072,3479212916736,
%T A188456 6113821454237696,23602899265140031488,198562423940692641316864,
%U A188456 3615246879908004653107773440,141631725381846630255125115961344
%N A188456 G.f.: 1 = Sum_{n>=0} a(n)*x^n*(1 - 2^n*x)^(n+1).
%C A188456 G.f. satisfies a variant of an identity of the Catalan numbers (A000108):
%C A188456 1 = Sum_{n>=0} A000108(n)*x^n*(1 - x)^(n+1).
%F A188456 0 = Sum_{k=0..[(n+1)/2]} (-1)^k*C(n-k+1,k)*2^(k*(n-k))*a(n-k) for n > 0.
%e A188456 G.f.: 1 = (1-x) + x*(1-2*x)^2 + 4*x^2*(1-4*x)^3 + 44*x^3*(1-8*x)^4 + 1216*x^4*(1-16*x)^5 + 80640*x^5*(1-32*x)^6 + ...
%t A188456 a[0] = 1; a[n_] := a[n] = SeriesCoefficient[1-Sum[a[k]*x^k*(1-2^k*x)^(k+1), {k, 0, n-1}], {x, 0, n}];
%t A188456 Table[a[n], {n, 0, 13}] (* _Jean-François Alcover_, Dec 09 2017 *)
%o A188456 (PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-2^k*x+x*O(x^n))^(k+1)), n)}
%Y A188456 Cf. A188455, A188457, A188458.
%K A188456 nonn
%O A188456 0,3
%A A188456 _Paul D. Hanna_, Mar 31 2011