%I A128771
%S A128771 1,2,0,0,2,0,0,0,0,0,4,0,0,4,0,0,2,0,0,8,0,0,8,0,0,2,0,0,16,0,0,16,0,0,
%T A128771 4,0,0,28,0,0,28,0,0,8,0,0,48,0,0,46,0,0,12,0,0,80,0,0,76,0,0,20,0,0,
%U A128771 126,0,0,120,0,0,32,0,0,196,0,0,184,0,0,48,0,0,300,0,0,280,0,0,72,0,0
%V A128771 1,-2,0,0,2,0,0,0,0,0,-4,0,0,4,0,0,2,0,0,-8,0,0,8,0,0,2,0,0,-16,0,0,16,
               0,0,4,0,0,-28,0,
%W A128771 0,28,0,0,8,0,0,-48,0,0,46,0,0,12,0,0,-80,0,0,76,0,0,20,0,0,-126,0,0,120,
               0,0,32,0,0,
%X A128771 -196,0,0,184,0,0,48,0,0,-300,0,0,280,0,0,72,0,0
%N A128771 Expansion of phi(-q)/phi(-q^9) in powers of q where phi() is a Ramanujan 
               theta function.
%F A128771 Expansion of eta(q)^2* eta(q^18)/( eta(q^2)* eta(q^9)^2 ) in powers of 
               q.
%F A128771 Euler transform of period 18 sequence [ -2, -1, -2, -1, -2, -1, -2, -1, 
               0, -1, -2, -1, -2, -1, -2, -1, -2, 0, ...].
%F A128771 G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (1-u)* (u-v^2) 
               -2*u* (v-1).
%F A128771 G.f. A(x) satisfies 0= f(A(x), A(x^3)) where f(u, v)= (u-v)^3 -u* (3-u)* 
               (v-1)* (3 -2*u +u*v).
%F A128771 G.f.: Product_{k>0} (1-x^k)* (1+x^(9k))/( (1+x^k)* (1-x^(9k)) ).
%F A128771 a(3n+2)= a(3n+3)= 0.
%o A128771 (PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^oo); polcoeff( eta(x+A)^2* 
               eta(x^18+A)/ eta(x^2+A)/ eta(x^9+A)^2, n))}
%Y A128771 Convolution inverse of A128770. -2*A092848(n)= a(3n+1).
%Y A128771 Sequence in context: A127826 A109983 A093492 this_sequence A139380 A000122 
               A002448
%Y A128771 Adjacent sequences: A128768 A128769 A128770 this_sequence A128772 A128773 
               A128774
%K A128771 sign
%O A128771 0,2
%A A128771 Michael Somos, Mar 27 2007