OFFSET
0,5
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
M. Ishikawa and J. Zeng, The Andrews-Stanley partition function and Al-Salam-Chihara polynomials, Disc. Math., 309 (2009), 151-175.
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
From Michael Somos, Jun 04 2012: (Start)
Expansion of chi(x) / f(x^2) in powers of x where chi(), f() are Ramanujan theta functions.
Expansion of q^(1/8) * eta(q^2)^3 * eta(q^8) / (eta(q) * eta(q^4)^4) in powers of q.
Euler transform of period 8 sequence [ 1, -2, 1, 2, 1, -2, 1, 1, ...]. (End)
EXAMPLE
G.f. = 1 + x - x^2 + 3*x^4 + 2*x^5 - 3*x^6 - x^7 + 8*x^8 + 5*x^9 - 8*x^10 + ...
G.f. = 1/q + q^7 - q^15 + 3*q^31 + 2*q^39 - 3*q^47 - q^55 + 8*q^63 + 5*q^71 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q^2]^3*(QP[q^8]/(QP[q]*QP[q^4]^4)) + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015, adapted from PARI *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^8 + A) / (eta(x + A) * eta(x^4 + A)^4), n))}; /* Michael Somos, Jun 04 2012 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Jan 02 2009
STATUS
approved