OFFSET
0,5
LINKS
Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
FORMULA
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.
EXAMPLE
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 - ...
MATHEMATICA
nmax = 48; Im[CoefficientList[Series[1/(1 + ContinuedFractionK[I x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]]
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]]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 04 2017
STATUS
approved