OFFSET
0,14
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 G(x^8) * H(x^3) - x * G(x^3) * H(x^8) in powers of x where G(), H() are Rogers-Ramanujan functions.
Expansion of q^(-5/12) * eta(q) * eta(q^4) * eta(q^6) * eta(q^24) / (eta(q^2) * eta(q^3) * eta(q^8) * eta(q^12)) in powers of q.
Euler transform of period 24 sequence [-1, 0, 0, -1, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, ...].
EXAMPLE
G.f. = 1 - x - x^4 + x^6 - x^7 + x^8 + x^9 - x^10 + x^12 - 2*x^13 + ...
G.f. = q^5 - q^17 - q^53 + q^77 - q^89 + q^101 + q^113 - q^125 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] QPochhammer[ x^4, x^8] QPochhammer[ -x^3, x^3] QPochhammer[ -x^12, x^12], {x, 0, n}];
PROG
(PARI) {a(n) = if( n<0, 0, my(A = x * O(x^n)); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^24 + A) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^8 + A) * eta(x^12 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jan 28 2017
STATUS
approved