A145705 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, 39, 44, -42, -41, 47, 54, -52, -49, 56, 64, -62, -59, 68, 79, -77, -72

Offset: 0

Author

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

Keywords

• sign

Examples

			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

(-1)^n * A145704(n) = a(n). A145706(n) = a(2*n). - A145707(n) = a(2*n + 1).

Programs

Mathematica

QP = QPochhammer; s = (QP[q^8]*QP[q^10]-q*QP[q^2]*QP[q^40])/(QP[q^4]* QP[q^20]) + O[q]^90; CoefficientList[s, q] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *)

PARI

{a(n) = local(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

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

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