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^(1/6) * eta(q)^2 * eta(q^4)^2 * eta(q^12)^3 / (eta(q^2) * eta(q^8)^6) in powers of q.
Euler transform of period 24 sequence [ -2, -1, -2, -3, -2, -1, -2, 3, -2, -1, -2, -6, -2, -1, -2, 3, -2, -1, -2, -3, -2, -1, -2, 0, ...].
EXAMPLE
G.f. = 1 - 2*x + 4*x^5 + x^8 - 12*x^9 - 3*x^12 + 30*x^13 + 4*x^16 + ...
G.f. = q^-1 - 2*q^5 + 4*q^29 + q^47 - 12*q^53 - 3*q^71 + 30*q^77 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^5 QPochhammer[ x^12]^3 / (QPochhammer[ -x]^2 QPochhammer[ x^8]^6), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^12 + A)^3 / (eta(x^2 + A) * eta(x^8 + A)^6), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 13 2015
STATUS
approved