%I A134747
%S A134747 1,8,28,64,142,352,792,1536,2917,5744,10868,19200,33414,58816,101256,
%T A134747 167936,275314,452392,732748,1160064,1819808,2851104,4421064,6752256,
%U A134747 10236407,15476272,23215192,34450944,50811638,74701632,109138272
%V A134747 1,-8,28,-64,142,-352,792,-1536,2917,-5744,10868,-19200,33414,-58816,101256,
               -167936,
%W A134747 275314,-452392,732748,-1160064,1819808,-2851104,4421064,-6752256,10236407,
               -15476272,
%X A134747 23215192,-34450944,50811638,-74701632,109138272
%N A134747 Expansion of q * (chi(-q) / chi(-q^4))^8 in powers of q where chi() is 
               a Ramanujan theta function.
%F A134747 Expansion of k * (1 - k) / ( 4 * (1 + k) ) in powers of q^(1/2) where 
               q is Jacobi's nome and k is the elliptic modulus.
%F A134747 Expansion of ( (eta(q) * eta(q^8)) / (eta(q^2) * eta(q^4)) )^8 in powers 
               of q.
%F A134747 Euler transform of period 8 sequence [ -8, 0, -8, 8, -8, 0, -8, 0, ...].
%F A134747 G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = 16 
               * u*w * (v*w-1) * (v*u-1) - (v - u^2) * (v - w^2).
%F A134747 G.f. is Fourier series of a weight 0 level 8 modular form. f(-1/(8 t)) 
               = f(t) where q = exp(2 pi i t).
%F A134747 G.f.: x * ( Product_{k>0} (1 + x^(4*k)) / (1 + x^k) )^8.
%e A134747 q - 8*q^2 + 28*q^3 - 64*q^4 + 142*q^5 - 352*q^6 + 792*q^7 - 1536*q^8 
               + ...
%o A134747 (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( ( 
               (eta(x + A) * eta(x^8 + A)) / (eta(x^2 + A) * eta(x^4 + A)) )^8, 
               n))}
%Y A134747 Convolution invserse of A131123.
%Y A134747 Sequence in context: A002408 A101127 A007259 this_sequence A083013 A028553 
               A100182
%Y A134747 Adjacent sequences: A134744 A134745 A134746 this_sequence A134748 A134749 
               A134750
%K A134747 sign
%O A134747 1,2
%A A134747 Michael Somos, Nov 07 2007