cp's OEIS Frontend

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.

%I A145705 #13 Mar 05 2018 04:10:12
%S A145705 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,
%T A145705 -4,-4,5,6,-6,-5,6,8,-7,-6,8,11,-10,-8,11,13,-11,-10,13,16,-15,-14,17,
%U A145705 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
%N 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.
%H A145705 G. C. Greubel, <a href="/A145705/b145705.txt">Table of n, a(n) for n = 0..1000</a>
%F A145705 Denoted by "(160~a)" in Simon Norton's replicable function list.
%F A145705 G.f. is a period 1 Fourier series which satisfies f(-1 / (1280 t)) = f(t) where q = exp(2 Pi i t).
%e A145705 1/q - q^3 + q^11 + q^15 + q^27 + q^31 - q^35 - q^39 + q^43 + 2*q^47 + ...
%t A145705 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 *)
%o A145705 (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))}
%Y A145705 (-1)^n * A145704(n) = a(n). A145706(n) = a(2*n). - A145707(n) = a(2*n + 1).
%K A145705 sign
%O A145705 0,13
%A A145705 _Michael Somos_, Oct 17 2008, Nov 11 2008, Jan 21 2009