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 A206740 #11 Aug 24 2017 17:08:52
%S A206740 1,1,1,1,2,3,4,6,9,13,20,30,44,66,99,147,220,329,490,732,1095,1634,
%T A206740 2440,3646,5444,8130,12146,18139,27089,40463,60434,90258,134811,
%U A206740 201349,300721,449153,670844,1001939,1496467,2235080,3338227,4985868,7446739,11122179
%N A206740 G.f.: 1/(1 - x/(1 - x^3/(1 - x^6/(1 - x^10/(1 - x^15/(1 - x^21/(1 -...- x^(n*(n+1)/2)/(1 -...))))))), a continued fraction.
%F A206740 G.f.: 1/Q(0) , where Q(k) = 1 - x^((2*k+1)*(2*k+2)/2)/(1 - x^((2*k+2)*(2*k+3)/2)/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Sep 10 2013
%F A206740 a(n) ~ c * d^n, where d = 1.49356638691558702616975760297981328... and c = 0.35853801643147450974166770910994348... - _Vaclav Kotesovec_, Aug 24 2017
%e A206740 G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 + 9*x^8 +...
%t A206740 nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[x^(Range[nmax + 1]*(Range[nmax + 1] + 1)/2)]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 24 2017 *)
%o A206740 (PARI) {a(n)=local(CF=1+x*O(x^n),M=sqrtint(n+1)); for(k=0, M, CF=1/(1-x^((M-k+1)*(M-k+2)/2)*CF)); polcoeff(CF, n, x)}
%o A206740 for(n=0,55,print1(a(n),", "))
%Y A206740 Cf. A206739.
%K A206740 nonn
%O A206740 0,5
%A A206740 _Paul D. Hanna_, Feb 12 2012