%I A137566
%S A137566 1,1,0,0,0,1,2,2,1,0,0,2,5,5,2,0,1,5,10,10,5,1,2,10,20,20,10,2,5,20,36,
%T A137566 36,20,6,10,36,65,65,36,12,21,65,110,110,65,25,38,110,185,185,110,46,70,
%U A137566 185,300,300,186,85,120,300,481,481,302,146,205,482,752,752,486,250
%V A137566 1,-1,0,0,0,-1,2,-2,1,0,0,-2,5,-5,2,0,1,-5,10,-10,5,-1,2,-10,20,-20,10,
               -2,5,-20,36,-36,
%W A137566 20,-6,10,-36,65,-65,36,-12,21,-65,110,-110,65,-25,38,-110,185,-185,110,
               -46,70,-185,
%X A137566 300,-300,186,-85,120,-300,481,-481,302,-146,205,-482,752,-752,486,-250
%N A137566 Expansion of q^(1/6) * eta(q) / ( eta(q^2) * eta(q^3) ) in powers of 
               q.
%F A137566 Euler transform of period 6 sequence [ -1, 0, 0, 0, -1, 1, ...].
%F A137566 G.f. is a period 1 Fourier series which satisfies f(-1 / (864 t)) = 24^(-1/
               2) (t/i)^(-1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for 
               A007690.
%F A137566 G.f.: (Product_{k>0} (1 + x^k) * (1 - x^(3*k)))^(-1).
%e A137566 q^-1 - q^5 - q^29 + 2*q^35 - 2*q^41 + q^47 - 2*q^65 + 5*q^71 + ...
%o A137566 (PARI) {a(n) = local(A); if( n<0, 0, A =x * O(x^n); polcoeff( eta(x + 
               A) / eta(x^2 + A) / eta(x^3 + A), n))}
%Y A137566 Sequence in context: A133418 A029390 A108040 this_sequence A122865 A074080 
               A111407
%Y A137566 Adjacent sequences: A137563 A137564 A137565 this_sequence A137567 A137568 
               A137569
%K A137566 sign
%O A137566 0,7
%A A137566 Michael Somos, Jan 26 2008