OFFSET
0,2
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 q^(-5/24) * eta(q)^2 * eta(q^3)^3 * eta(q^4)^2 / eta(q^2)^7 in power of q.
Euler transform of period 12 sequence [ -2, 5, -5, 3, -2, 2, -2, 3, -5, 5, -2, 0, ...].
a(n) ~ (-1)^n * exp(Pi*sqrt(3*n/2)) / (2^(11/4) * 3^(5/4) * n^(3/4)). - Vaclav Kotesovec, Sep 23 2015
EXAMPLE
G.f. = 1 - 2*x + 6*x^2 - 15*x^3 + 33*x^4 - 68*x^5 + 134*x^6 - 253*x^7 + ...
G.f. = q^5 - 2*q^29 + 6*q^53 - 15*q^77 + 33*q^101 - 68*q^125 + 134*q^149 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 / (QPochhammer[ -x]^2 QPochhammer[ x^2]), {x, 0, n}];
nmax = 40; CoefficientList[Series[Product[(1-x^(3*k))^3 * (1+x^(2*k))^2 / ((1-x^k)^3 * (1+x^k)^5), {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 + A)^2 * eta(x^3 + A)^3 * eta(x^4 + A)^2 / eta(x^2 + A)^7, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 13 2015
STATUS
approved