OFFSET
0,8
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^(-7/12) * eta(q^2) * eta(q^3) * eta(q^4) * eta(q^12) /
(eta(q) * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 1, 0, 0, -1, 1, 0, 1, -1, 0, 0, 1, -2, ...].
2*a(n) = A093829(12*n + 7).
EXAMPLE
G.f. = 1 + x + x^2 + x^3 + x^5 + x^6 + 2*x^7 + x^8 + x^10 + x^11 + ...
G.f. = q^7 + q^19 + q^31 + q^43 + q^67 + q^79 + 2*q^91 + q^103 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x^1, x^6] QPochhammer[ -x^5, x^6] QPochhammer[ x^6] EllipticTheta[ 2, 0, x] / (2 x^(1/4)), {x, 0, n}]; (* Michael Somos, Sep 02 2014 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^6 + A)), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 16 2006
STATUS
approved