OFFSET
0,2
COMMENTS
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
FORMULA
Expansion of (eta(q)^2 * eta(q^2) * eta(q^8)^2 / eta(q^4)^5)^2 in powers of q.
Euler transform of period 8 sequence [ -4, -6, -4, 4, -4, -6, -4, 0, ...].
a(n) = (-1)^n * A134746(n).
Empirical: Sum_{n>=0} a(n)/exp(2*Pi*n) = -32 - 24*sqrt(2) + 4*sqrt(140+99*sqrt(2)). - Simon Plouffe, Mar 02 2021
EXAMPLE
1 - 4*q + 16*q^3 - 56*q^5 + 160*q^7 - 404*q^9 + 944*q^11 - 2072*q^13 + ...
MATHEMATICA
a[n_] := SeriesCoefficient[(EllipticTheta[3, 0, -q]/EllipticTheta[3, 0, q^2])^2, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Nov 29 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^2 * eta(x^2 + A) * eta(x^8 + A)^2 / eta(x^4 + A)^5)^2, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 16 2012
STATUS
approved