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 A208236 #11 Nov 03 2014 03:53:44
%S A208236 1,1,1,4,10,50,208,1290,7456,55982,411796,3650514,32484460,332970374,
%T A208236 3468625588,40420787250,481757564956,6295577910182,84407459209876,
%U A208236 1223095585594674,18208380720893980,289843786627539014,4741844351895315028,82269590167564595250
%N A208236 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1 + n*k*x) / (1 + x + n*k*x^2).
%C A208236 Compare to the identity:
%C A208236 Sum_{n>=0} x^n * Product_{k=1..n} (1 + t*k*x) / (1 + x + t*k*x^2) = (1+x)/(1-t*x^2).
%C A208236 Compare to the g.f. of A187741:
%C A208236 Sum_{n>=0} x^n * (1 + n*x)^n / (1 + x + n*x^2)^n = 1/2 + (1+2*x)*Sum_{n>=0} (n+1)!*x^(2*n)/2.
%C A208236 Limit n->infinity (a(n)/n!)^(1/n) = 1/(2*log(2)). - _Vaclav Kotesovec_, Nov 03 2014
%H A208236 Vaclav Kotesovec, <a href="/A208236/b208236.txt">Table of n, a(n) for n = 0..200</a>
%e A208236 G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 10*x^4 + 50*x^5 + 208*x^6 + 1290*x^7 +...
%e A208236 where
%e A208236 A(x) = 1 + x*(1+x)/(1+x+x^2) + x^2*(1+2*1*x)*(1+2*2*x)/((1+x+2*1*x^2)*(1+x+2*2*x^2)) + x^3*(1+3*1*x)*(1+3*2*x)*(1+3*3*x)/((1+x+3*1*x^2)*(1+x+3*2*x^2)*(1+x+3*3*x^2)) + x^4*(1+4*1*x)*(1+4*2*x)*(1+4*3*x)*(1+4*4*x)/((1+x+4*1*x^2)*(1+x+4*2*x^2)*(1+x+4*3*x^2)*(1+x+4*4*x^2)) +...
%o A208236 (PARI) {a(n)=polcoeff( sum(m=0, n, x^m*prod(k=1, m, (1+m*k*x)/(1+x+m*k*x^2 +x*O(x^n))) ), n)}
%o A208236 for(n=0, 30, print1(a(n), ", "))
%Y A208236 Cf. A204064, A187741, A204066.
%K A208236 nonn
%O A208236 0,4
%A A208236 _Paul D. Hanna_, Jan 10 2013