A293268 - OEIS

%I #6 Oct 04 2017 18:39:41

%S 1,0,-1,-1,1,3,2,-2,-7,-6,4,16,14,-9,-37,-33,20,87,82,-41,-201,-198,

%T 85,465,475,-178,-1084,-1150,353,2511,2767,-684,-5810,-6633,1287,

%U 13463,15923,-2222,-31119,-38130,3356,71838,91138,-3595,-165763,-217705,-1761,381895,519284,27984,-878685

%N G.f.: Re(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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>

%F G.f.: Re( (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 G.f. A(x) = Sum_{n>=0} (a(n) + i*A293269(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 nmax = 50; Re[CoefficientList[Series[1/(1 + ContinuedFractionK[I x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]]

%t nmax = 50; Re[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 Cf. A007325, A278399, A292136, A293269.

%K sign

%O 0,6

%A _Ilya Gutkovskiy_, Oct 04 2017