OFFSET
-1,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of eta(q^2)^2 * eta(q^3)^3 / (eta(q) * eta(q^6)^6) in powers of q.
Euler transform of period 6 sequence [1, -1, -2, -1, 1, 2, ...].
G.f.: x^-1 * Product_{k>0} ((1 - x^(2*k))^2 * (1 - x^(3*k))^3) / ((1 - x^k) * (1 - x^(6*k))^6).
EXAMPLE
G.f. = 1/q + 1 - 2*q^2 - 3*q^3 + 4*q^5 + 6*q^6 - 10*q^8 - 12*q^9 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/q) QPochhammer[ q^2]^2 QPochhammer[ q^3]^3 / (QPochhammer[ q] QPochhammer[ q^6]^6), {q, 0, n}]; (* Michael Somos, May 25 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 / (eta(x + A) * eta(x^6 + A)^6), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, May 19 2015
STATUS
approved