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 A302016 #7 Feb 16 2025 08:33:53
%S A302016 1,1,2,3,4,6,9,14,21,31,46,68,102,153,229,342,510,761,1136,1697,2535,
%T A302016 3786,5653,8441,12605,18824,28112,41981,62691,93617,139800,208768,
%U A302016 311761,465564,695242,1038226,1550415,2315284,3457489,5163181,7710344,11514102,17194374,25676907,38344147
%N A302016 Expansion of 1/(1 - x - x^2/(1 + x^2/(1 + x^3/(1 + x^4/(1 + x^5/(1 + ...)))))), a continued fraction.
%H A302016 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A302016 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%F A302016 G.f.: 1/(1 - x*Product_{k>=1} (1 - x^(5*k-2))*(1 - x^(5*k-3))/((1 - x^(5*k-1))*(1 - x^(5*k-4)))).
%F A302016 a(0) = 1; a(n) = Sum_{k=1..n} A003823(k-1)*a(n-k).
%F A302016 a(n) ~ c / r^n, where r = 0.669643458685499460127124120930664114507093547265881... is the root of the equation x*QPochhammer[x^2, x^5]*QPochhammer[x^3, x^5] = QPochhammer[x, x^5]*QPochhammer[x^4, x^5] and c = 0.833333547701931811823757549354805979633827853516233646128015838266... - _Vaclav Kotesovec_, Jun 08 2019
%t A302016 nmax = 44; CoefficientList[Series[1/(1 - x - x^2/(1 + ContinuedFractionK[x^k, 1, {k, 2, nmax}])), {x, 0, nmax}], x]
%t A302016 nmax = 44; CoefficientList[Series[1/(1 - x QPochhammer[x^2, x^5] QPochhammer[x^3, x^5]/(QPochhammer[x, x^5] QPochhammer[x^4, x^5])), {x, 0, nmax}], x]
%Y A302016 Antidiagonal sums of A291678.
%Y A302016 Cf. A003823, A302015.
%K A302016 nonn
%O A302016 0,3
%A A302016 _Ilya Gutkovskiy_, Mar 30 2018