OFFSET
0,3
COMMENTS
REFERENCES
Bruce C. Berndt, Ramanujan's Notebooks, Part IV, Springer-Verlag, 1984; see Entry 27, pp. 170-171. This is the corrected left side of (27.1), divided by 4.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
EXAMPLE
G.f. = 1 + 4*x^2 + 4*x^4 + 8*x^8 + 4*x^9 + 16*x^10 + 12*x^11 + 8*x^13 + ...
G.f. = 1 + 4*q^4 + 4*q^8 + 8*q^16 + 4*q^18 + 16*q^20 + 12*q^22 + 8*q^26 + 4*q^28 + ...
MATHEMATICA
f[q_] := QPochhammer[-q, -q]; p[q_] := EllipticTheta[3, 0, q]; u[q_] := (1/2)*q^(-1/8)*EllipticTheta[2, 0, Sqrt[q]]; A170773[n_] := SeriesCoefficient[(1/2)*(p[q]*p[q^7]*p[q^9]*p[q^63] + p[-q]*p[-q^7]*p[-q^9]*p[-q^63] + 4*q^4*f[-q^6]^2*f[-q^42]^2 + 16*q^20*u[q^2]*u[q^14]*u[q^18]*u[q^(126)]), {q, 0, n}]; Table[A170773[n], {n, 0, 100}][[ ;; ;; 2]] (* G. C. Greubel, Dec 03 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Dec 10 2009
STATUS
approved