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)^5 * eta(q^16)^2 / (eta(q)^2 * eta(q^8)^5))^2 in powers of q.
Euler transform of period 16 sequence [ 4, -6, 4, -6, 4, -6, 4, 4, 4, -6, 4, -6, 4, -6, 4, 0, ...].
Convolution square of A208274.
Empirical: Sum{n>=0} a(n)/exp(Pi*n) = 40 + 28*sqrt(2) - 8*sqrt(48+34*sqrt(2)). - Simon Plouffe, Mar 02 2021
EXAMPLE
1 + 4*q + 4*q^2 - 8*q^5 - 16*q^6 + 20*q^9 + 56*q^10 - 40*q^13 - 160*q^14 + ...
MATHEMATICA
a[n_]:= SeriesCoefficient[(EllipticTheta[3, 0, q]/EllipticTheta[3, 0, q^4])^2, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Dec 04 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 * eta(x^16 + A)^2 / (eta(x + A)^2 * eta(x^8 + A)^5))^2, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 31 2012
STATUS
approved