%I A128764
%S A128764 1,1,0,1,1,1,1,1,2,2,2,2,3,2,2,4,4,4,4,5,6,6,6,7,9,9,10,12,12,13,14,16,
%T A128764 18,19,20,23,26,26,28,30,33,37,38,42,46,49,52,56,62,65,70,76,84,89,92,
%U A128764 101,110,117,123,133,145,153,162,174,188,197,208,227,242,256,270,290
%N A128764 Expansion of chi(q)/ chi(q^13) in powers of q where chi() is a Ranaujan 
               theta function.
%F A128764 Given g.f. A(x), then B(x)= x*A(x^2) satisfies 0= f(B(x), B(x^3)) where 
               f(u, v)= (u-v^3)* (u^3-v) -3*u*v* (u^2+v^2 -u*v).
%F A128764 Euler transform of period 52 sequence [ 1, -1, 1, 0, 1, -1, 1, 0, 1, 
               -1, 1, 0, 0, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1, -1, 
               1, 0, 1, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 
               1, 0, ...].
%F A128764 G.f.: Product_{k>0} (1+x^k)* (1+x^(26k))/( (1+x^(2k))* (1+x^(13k)) ).
%e A128764 q + q^3 + q^7 + q^9 + q^11 + q^13 + q^15 + 2*q^17 + 2*q^19 + ...
%o A128764 (PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2* 
               eta(x^13+A)* eta(x^52+A)/ (eta(x+A)* eta(x^4+A)* eta(x^26+A)^2), 
               n))}
%Y A128764 Sequence in context: A067595 A134868 A127417 this_sequence A074589 A165035 
               A081309
%Y A128764 Adjacent sequences: A128761 A128762 A128763 this_sequence A128765 A128766 
               A128767
%K A128764 nonn
%O A128764 0,9
%A A128764 Michael Somos, Mar 25 2007