%I A117410
%S A117410 1,1,1,0,1,2,1,1,1,0,1,1,1,1,0,2,1,0,0,1,2,1,0,1,0,1,0,1,1,1,3,0,1,1,1,
%T A117410 1,0,0,0,1,2,0,1,0,1,0,1,0,0,1,2,1,0,1,1,3,0,1,0,1,1,0,1,0,0,2,0,1,1,0,
%U A117410 2,1,1,0,0,1,0,0,1,1,0,1,1,1,0,2,1,0,2,1,2,0,1,1,0,2,1,1,1,1,0,0,0,1,0
%V A117410 1,1,-1,0,-1,-2,1,-1,-1,0,1,1,-1,1,0,2,1,0,0,-1,2,1,0,-1,0,-1,0,-1,1,1,
               -3,0,-1,-1,-1,1,
%W A117410 0,0,0,-1,-2,0,1,0,1,0,1,0,0,-1,2,-1,0,1,1,3,0,-1,0,1,-1,0,1,0,0,2,0,1,
               -1,0,-2,-1,1,0,
%X A117410 0,-1,0,0,1,-1,0,-1,-1,-1,0,-2,-1,0,2,1,-2,0,1,-1,0,-2,-1,1,-1,1,0,0,0,
               1,0
%N A117410 Expansion of q^(-5/24) eta(q^2)^3/eta(q) in powers of q.
%D A117410 B. Gordon and D. Sinor, Multiplicative properties of eta-products, Number 
               theory, Madras 1987, pp. 173-200, Lecture Notes in Math., 1395, Springer, 
               Berlin, 1989. see page 183. MR1019331 (90k:11050)
%F A117410 Euler transform of period 2 sequence [ 1, -2, ...].
%F A117410 Given A=A0+A1+A2+Ae is the 5-section, then 0=A3*A1^2-A2*A4^2.
%F A117410 Given A=A0+A1+A2+A3+A4+A5+A6 is the 7-section, then 0=A0*A6+A1*A5+A2*A4+4*A3^2, 
               A3=x^10*A(x^49).
%F A117410 G.f. Product_{k>0} (1+x^k)(1-x^(2k))^2.
%o A117410 (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^3/
               eta(x+A), n))}
%Y A117410 Cf. A107034(n)=(-1)^n*a(n).
%Y A117410 Sequence in context: A117195 A156606 A107034 this_sequence A087810 A052314 
               A093718
%Y A117410 Adjacent sequences: A117407 A117408 A117409 this_sequence A117411 A117412 
               A117413
%K A117410 sign
%O A117410 0,6
%A A117410 Michael Somos, Mar 13 2006