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 psi(-x)^8 * chi(-x^2)^6 = f(-x)^8 / chi(-x^2)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, Sep 03 2013
Expansion of q^(-1/2) * (eta(q)^4 * eta(q^4) / eta(q^2))^2 in powers of q.
Euler transform of period 4 sequence [ -8, -6, -8, -8, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 2^15 (t/i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A225564. - Michael Somos, Sep 03 2013
Convolution square of A215597.
a(2*n) = A215601(n). - Michael Somos, Sep 03 2013
EXAMPLE
1 - 8*x + 22*x^2 - 16*x^3 - 27*x^4 + 40*x^5 - 18*x^6 + 80*x^7 - 94*x^8 + ...
q - 8*q^3 + 22*q^5 - 16*q^7 - 27*q^9 + 40*q^11 - 18*q^13 + 80*q^15 - 94*q^17 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q]^6 EllipticTheta[ 2, Pi/4, q^(1/2)]^2 / (2 q^(1/4)), {q, 0, n}] (* Michael Somos, Sep 03 2013 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ q]^8 / QPochhammer[ q^2, q^4]^2, {q, 0, n}] (* Michael Somos, Sep 03 2013 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^4 * eta(x^4 + A) / eta(x^2 + A))^2, n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 16 2012
STATUS
approved