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^(-2/3) * (eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 / (eta(q) * eta(q^4) * eta(q^6)^6))^2 in powers of q.
Euler transform of period 12 sequence [ 2, -2, -4, 0, 2, 4, 2, 0, -4, -2, 2, 0, ...].
Convolution square of A128111.
EXAMPLE
G.f. = 1 + 2*x + x^2 - 4*x^3 - 8*x^4 - 2*x^5 + 14*x^6 + 24*x^7 + 6*x^8 + ...
G.f. = q^2 + 2*q^5 + q^8 - 4*q^11 - 8*q^14 - 2*q^17 + 14*q^20 + 24*q^23 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[(QPochhammer[-q, q^2]/(QPochhammer[-q^3, q^6])^3)^2, {q, 0, n}]; (* Michael Somos, Sep 02 2015 *)(* Corrected by G. C. Greubel_, Aug 10 2017 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^6))^2, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 17 2009
STATUS
approved