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 A293269 #10 Mar 14 2025 06:21:15
%S A293269 0,-1,0,1,2,0,-3,-5,-1,7,12,3,-16,-27,-7,37,64,20,-85,-152,-55,191,
%T A293269 356,141,-436,-841,-364,991,1988,938,-2233,-4674,-2369,5044,11004,
%U A293269 5963,-11361,-25898,-14959,25467,60821,37245,-56995,-142783,-92384,127136,334946,228385,-282392
%N A293269 G.f.: Im(1/(1 + i*x/(1 + i*x^2/(1 + i*x^3/(1 + i*x^4/(1 + i*x^5/(1 + ...))))))), a continued fraction, where i is the imaginary unit.
%H A293269 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%F A293269 G.f.: Im( (Sum_{k>=0} i^k*x^(k*(k+1))/Product_{m=1..k} (1 - x^m)) / (Sum_{k>=0} i^k*x^(k^2)/Product_{m=1..k} (1 - x^m)) ), where i is the imaginary unit.
%e A293269 G.f. A(x) = Sum_{n>=0} (A293268(n) + i*a(n))*x^n = 1 - i*x - x^2 - (1 - i)*x^3 + (1 + 2*i)*x^4 + 3*x^5 + (2 - 3*i)*x^6 - (2 + 5*i)*x^7 - (7 + i)*x^8 - ...
%t A293269 nmax = 48; Im[CoefficientList[Series[1/(1 + ContinuedFractionK[I x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]]
%t A293269 nmax = 48; Im[CoefficientList[Series[Sum[I^k x^(k (k + 1)) / Product[1 - x^m, {m, 1, k}], {k, 0, nmax}] / Sum[I^k x^(k^2) / Product[1 - x^m, {m, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]]
%Y A293269 Cf. A007325, A278400, A292137, A293268.
%K A293269 sign
%O A293269 0,5
%A A293269 _Ilya Gutkovskiy_, Oct 04 2017