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 A355040 #19 Jun 26 2022 09:31:55
%S A355040 1,1,2,5,13,35,96,266,742,2079,5843,16457,46423,131099,370527,1047858,
%T A355040 2964698,8390837,23754234,67260645,190478213,539484321,1528094423,
%U A355040 4328632609,12262352881,34738763766,98416624789,278825903115,789961599608,2238129694407,6341171821627,17966261019890,50903653156245
%N A355040 Expansion of the continued fraction 1 / (1-q / (1-q-q^2 / (1-q-q^2-q^3 / (1-q-q^2-q^3-q^4 / (...))))).
%F A355040 a(n) ~ c * d^n, where d = 2.8333645039948803621658813720055524872119... and c = 0.1710130167563241590871776261530008679... - _Vaclav Kotesovec_, Jun 16 2022
%F A355040 a(n) = [q^n] K_{k>=0} -q^k / ((q^(k + 1) - 2*q + 1)/(q - 1)), where K is Gauss's notation for continued fractions. - _Peter Luschny_, Jun 20 2022
%t A355040 nmax = 40; CoefficientList[Series[1/(1 - x/(1 - x + ContinuedFractionK[-x^k, 1 - x*(1 - x^k)/(1 - x), {k, 2, nmax}])), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2022 *)
%t A355040 A355040List[nmax_] := Module[{a, b, q},
%t A355040 a = ContinuedFractionK[-q^k, (q^(k + 1) - 2 q + 1)/(q - 1), {k, 0, nmax}];
%t A355040 b = Series[a, {q, 0, nmax}]; CoefficientList[b, q] ];
%t A355040 A355040List[32] (* _Peter Luschny_, Jun 20 2022 *)
%o A355040 (PARI) N=44; q='q+O('q^N);
%o A355040 f(n) = 1 - sum(k=1,n-1,q^k);
%o A355040 s=1; forstep(j=N, 1, -1, s = q^j/s; s = f(j) - s ); s = 1/s;
%o A355040 Vec(s)
%Y A355040 Cf. A230823, A355043, A355046.
%Y A355040 Cf. A088354.
%K A355040 nonn
%O A355040 0,3
%A A355040 _Joerg Arndt_, Jun 16 2022