%I A135211
%S A135211 1,1,0,0,1,0,1,1,0,2,1,0,2,2,0,2,3,0,3,3,0,4,4,0,5,6,0,6,7,0,7,8,0,10,
%T A135211 10,0,13,13,0,14,16,0,17,18,0,22,22,0,26,28,0,30,33,0,36,38,0,44,45,0,
%U A135211 52,55,0,60,65,0,70,74,0,84,87,0,99,104,0,112,121,0,131,138,0,156,160
%V A135211 1,-1,0,0,-1,0,1,-1,0,2,-1,0,2,-2,0,2,-3,0,3,-3,0,4,-4,0,5,-6,0,6,-7,0,
               7,-8,0,10,-10,0,
%W A135211 13,-13,0,14,-16,0,17,-18,0,22,-22,0,26,-28,0,30,-33,0,36,-38,0,44,-45,
               0,52,-55,0,60,
%X A135211 -65,0,70,-74,0,84,-87,0,99,-104,0,112,-121,0,131,-138,0,156,-160
%N A135211 Expansion of q^(1/4) * eta(q) * eta(q^4) * eta(q^6) / ( eta(q^2) * eta(q^3) 
               * eta(q^12) ) in powers of q.
%F A135211 Expansion of psi(-q) / psi(-q^3) in powers of q where psi() is a Ramanujan 
               theta function.
%F A135211 Euler transform of period 12 sequence [ -1, 0, 0, -1, -1, 0, -1, -1, 
               0, 0, -1, 0, ...].
%F A135211 Given g.f. A(x), then B(x) = A(x^4) / x satisfies 0 = f(B(x), B(x^3)) 
               where f(u, v) = (1 + v^4) - (1 + u*v)^3.
%F A135211 G.f. is a period 1 Fourier series which satisfies f(-1 / (192 t)) = sqrt(3) 
               / f(t) where q = exp(2 pi i t).
%F A135211 a(3*n+2) = 0.
%e A135211 1/q - q^3 - q^15 + q^23 - q^27 + 2*q^35 - q^39 + 2*q^47 - 2*q^51 + ...
%o A135211 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x 
               + A) * eta(x^4 + A) * eta(x^6 + A) / (eta(x^2 + A) * eta(x^3 + A) 
               * eta(x^12 + A)), n))}
%Y A135211 -A036018(n) = a(3*n+1). Convolution inverse of A036018.
%Y A135211 Sequence in context: A146973 A003263 A157242 this_sequence A029294 A065434 
               A045832
%Y A135211 Adjacent sequences: A135208 A135209 A135210 this_sequence A135212 A135213 
               A135214
%K A135211 sign
%O A135211 0,10
%A A135211 Michael Somos, Nov 22 2007, Nov 23 2007