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 A206741 #16 Aug 25 2017 03:51:04
%S A206741 1,1,2,4,9,20,45,102,231,524,1189,2698,6124,13900,31551,71618,162566,
%T A206741 369013,837633,1901368,4315978,9796979,22238489,50479892,114585999,
%U A206741 260102617,590415686,1340204451,3042175244,6905536091,15675109089,35581458383,80767551510
%N A206741 G.f.: 1/(1 - x/(1 - x/(1 - x^2/(1 - x^3/(1 - x^5/(1 - x^8/(1 -...- x^Fibonacci(n)/(1 -...)))))))), a continued fraction.
%H A206741 Vaclav Kotesovec, <a href="/A206741/b206741.txt">Table of n, a(n) for n = 0..500</a>
%F A206741 a(n) ~ c * d^n, where d = 2.2699337019511296354569330617166782764872939098477919669570757033487700138... and c = 0.3272015736512679060779796519077970622372291004190408455581585307453... - _Vaclav Kotesovec_, Aug 25 2017
%e A206741 G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 45*x^6 + 102*x^7 +...
%t A206741 nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[x^(Fibonacci[Range[nmax + 1]])]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 25 2017 *)
%o A206741 (PARI) {a(n)=local(CF=1+x*O(x^n),M=ceil(log(n+1)/log(1.6))); for(k=0, M, CF=1/(1-x^fibonacci(M-k+1)*CF)); polcoeff(CF, n, x)}
%o A206741 for(n=0,50,print1(a(n),", "))
%Y A206741 Cf. A206742, A206743.
%K A206741 nonn
%O A206741 0,3
%A A206741 _Paul D. Hanna_, Feb 12 2012