OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-2/3) * eta(q) * eta(q^2) * eta(q^3) * eta(q^12)^4 / (eta(q^4)^2 * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [-1, -2, -2, 0, -1, -2, -1, 0, -2, -2, -1, -4, ...].
a(4*n) = 0. a(n) = -(-1)^n * A208435(n).
EXAMPLE
G.f. = x - x^2 - 2*x^3 + 3*x^5 + 2*x^6 - 4*x^7 + 5*x^9 - x^10 - 8*x^11 + ...
G.f. = q^5 - q^8 - 2*q^11 + 3*q^17 + 2*q^20 - 4*q^23 + 5*q^29 - q^32 - 8*q^35 + ...
MATHEMATICA
QP:= QPochhammer; Join[{0}, CoefficientList[Series[Simplify[QP[q]* QP[q^2]*QP[q^3]*QP[q^12]^4/(QP[q^4]^2*QP[q^6]), q > 0], {q, 0, 50}], q]] (* G. C. Greubel, Aug 12 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)^4 / (eta(x^4 + A)^2 * eta(x^6 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Feb 26 2012
STATUS
approved