OFFSET
0,3
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 (eta(q) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60)) / (eta(q^2) * eta(q^30))^3 in powers of q.
Euler transform of a period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Sep 05 2015
a(n) ~ (-1)^n * exp(2*Pi*sqrt(2*n/15)) / (2^(7/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
EXAMPLE
G.f. = 1 - q + 2*q^2 - 3*q^3 + 5*q^4 - 7*q^5 + 10*q^6 - 14*q^7 + 20*q^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q^6] QPochhammer[ q^10] / (QPochhammer[ -q] QPochhammer[ -q^15]), {q, 0, n}]; (* Michael Somos, Sep 05 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A)) / (eta(x^2 + A) * eta(x^30 + A))^3, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 23 2008
STATUS
approved