OFFSET
0,4
COMMENTS
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(1/24) * eta(q^3)^3 / (eta(q^2) * eta(q^4)^2) in powers of q.
Euler transform of period 12 sequence [ 0, 1, -3, 3, 0, -2, 0, 3, -3, 1, 0, 0, ...].
a(n) = A143066(3*n).
a(n) ~ (-1)^n * exp(Pi*sqrt(n/2)) / (2^(3/4) * 3^(3/2) * n^(3/4)). - Vaclav Kotesovec, Sep 13 2015
EXAMPLE
G.f. = 1 + x^2 - 3*x^3 + 4*x^4 - 3*x^5 + 5*x^6 - 12*x^7 + 14*x^8 + ...
G.f. = q^-1 + q^47 - 3*q^71 + 4*q^95 - 3*q^119 + 5*q^143 - 12*q^167 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 / (QPochhammer[ x^2] QPochhammer[ x^4]^2), {x, 0, n}];
nmax = 60; CoefficientList[Series[Product[(1-x^(3*k))^3 / ((1-x^(2*k))^3 * (1+x^(2*k))^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 13 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^3 / (eta(x^2 + A) * eta(x^4 + A)^2), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 13 2015
STATUS
approved