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 q^(-11/12) * eta(q^2)^3 * eta(q^3)^2 * eta(q^12)^2 / (eta(q)^2 * eta(q^6)^2) in powers of q.
Euler transform of period 12 sequence [ 2, -1, 0, -1, 2, -1, 2, -1, 0, -1, 2, -3, ...].
-2 * a(n) = A263527(4*n + 3).
EXAMPLE
G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + ...
G.f. = q^11 + 2*q^23 + 2*q^35 + 2*q^47 + q^59 + 2*q^71 + 3*q^83 + 4*q^95 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/2) x^(-3/4) EllipticTheta[ 2, Pi/4, x^(3/2)]^2 QPochhammer[ x^2]^3 / QPochhammer[ x]^2, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^3 + A)^2 * eta(x^12 + A)^2 / (eta(x + A)^2 * eta(x^6 + A)^2), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 29 2015
STATUS
approved