A145704 Expansion of q^(1/4) * (eta(q^8) * eta(q^10) + eta(q^2) * eta(q^40)) / (eta(q^4) * eta(q^20)) in powers of q.

1, 1, 0, -1, 1, 0, 0, -1, 1, 1, -1, -1, 2, 1, -1, -1, 2, 2, -1, -2, 3, 3, -2, -3, 4, 3, -2, -4, 5, 4, -4, -5, 6, 6, -5, -6, 8, 7, -6, -8, 11, 10, -8, -11, 13, 11, -10, -13, 16, 15, -14, -17, 20, 18, -17, -20, 24, 23, -21, -25, 31, 29, -26, -32, 37, 34, -32

Offset: 0

Author

Michael Somos, Oct 17 2008, Nov 11 2008, Jan 21 2009

Keywords

• sign

Comments

Denoted by "(160~b)" in Simon Norton's replicable function list.

Examples

			G.f. = 1 + x - x^3 + x^4 - x^7 + x^8 + x^9 - x^10 - x^11 + 2*x^12 + x^13 + ...
G.f. = 1/q + q^3 - q^11 + q^15 - q^27 + q^31 + q^35 - q^39 - q^43 + 2*q^47 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A145705, A145706, A145707.

Programs

Mathematica

a[ n_] := SeriesCoefficient[ (QPochhammer[ x^8] QPochhammer[ x^10] + x QPochhammer[ x^2] QPochhammer[ x^40]) / (QPochhammer[ x^4] QPochhammer[ x^20]), {x, 0, n}]; (* Michael Somos, Sep 06 2015 *)

PARI

{a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^8 + A) * eta(x^10 + A) + x * eta(x^2 + A) * eta(x^40 + A)) / (eta(x^4 + A) * eta(x^20 + A)), n))};

Formula

G.f. is a period 1 Fourier series which satisfies f(-1 / (1280 t)) = f(t) where q = exp(2 Pi i t).

a(n) = (-1)^n * A145705(n). a(2*n) = A145706(n). a(2*n + 1) = A145707(n).