%I A143251
%S A143251 1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,1,1,1,2,0,1,0,0,2,1,1,0,1,0,1,1,
%T A143251 0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,1,
%U A143251 0,0,2,1,0,1,1,0,0,1,0,0,1,1,0,1,0,2,1,0,1,2,0,0,0,0,1,0,0,1,1,1,0,0,0
%V A143251 1,-1,-1,1,0,0,-1,0,0,1,1,0,0,0,0,0,-1,0,0,-1,1,-1,2,0,-1,0,0,-2,-1,1,
               0,1,0,1,1,0,0,1,
%W A143251 0,-1,-1,0,0,1,0,-1,0,0,0,1,0,1,-1,0,-1,0,1,-1,-1,0,0,0,0,-1,0,-1,1,0,
               0,1,0,0,2,-1,0,1,
%X A143251 1,0,0,-1,0,0,-1,-1,0,-1,0,2,1,0,-1,2,0,0,0,0,1,0,0,-1,-1,-1,0,0,0
%N A143251 Expansion of f(-x, -x^7) * f(-x^2, -x^6) in powers of x where f(,) is 
               Ramanujan's two variable theta function.
%F A143251 Euler transform of period 8 sequence [ -1, -1, 0, 0, 0, -1, -1, -2, ...].
%F A143251 G.f.: Product_{k>0} (1 - x^(8*k))^2 * (1 - x^(8*k - 1)) * (1 - x^(8*k 
               - 2)) * (1 - x^(8*k - 6)) * (1 - x^(8*k - 7)).
%e A143251 q^13 - q^29 - q^45 + q^61 - q^109 + q^157 + q^173 - q^269 - q^317 + ...
%o A143251 (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^([2, 1, 1, 
               0, 0, 0, 1, 1][k%8 + 1]), 1 + x * O(x^n)), n))}
%Y A143251 Sequence in context: A104451 A106602 A106594 this_sequence A115235 A160973 
               A036853
%Y A143251 Adjacent sequences: A143248 A143249 A143250 this_sequence A143252 A143253 
               A143254
%K A143251 sign
%O A143251 0,23
%A A143251 Michael Somos, Aug 01 2008