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^(1/6) * eta(q)^2 / (eta(q^2) * eta(q^4)) in powers of q.
Euler transform of period 4 sequence [ -2, -1, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (576 t)) = 8^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A098613. - Michael Somos, Sep 07 2015
a(4*n + 2) = a(4*n + 3) = 0.
G.f.: (Product_{k>0} (1 + x^k)^2 * (1 + x^(2*k)))^-1.
EXAMPLE
G.f. = 1 - 2*x + 3*x^4 - 2*x^5 + 4*x^8 - 6*x^9 + 7*x^12 - 8*x^13 + 13*x^16 + ...
G.f. = 1/q - 2*q^5 + 3*q^23 - 2*q^29 + 4*q^47 - 6*q^53 + 7*q^71 - 8*q^77 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2]^2 QPochhammer[ x^2, x^4], {x, 0, n}]; (* Michael Somos, Sep 07 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 / (eta(x^2 + A) * eta(x^4 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 27 2008
STATUS
approved