Search: id:A116915
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%I A116915
%S A116915 1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
%T A116915 0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U A116915 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
%V A116915 1,-1,1,0,-1,0,0,0,0,0,0,-1,0,0,0,1,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
               0,0,0,0,1,0,0,0,
%W A116915 0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,-1,0,0,0,
%X A116915 0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0
%N A116915 Expansion of f(-x,-x^4)^2/f(-x,-x^2) in powers of x.
%C A116915 f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable 
               theta function.
%F A116915 Euler transform of period 5 sequence [ -1, 1, 1, -1, -1,...].
%F A116915 G.f.: Sum_{k} (-1)^k(x^((15k^2-7k)/2) -x^((15k^2+13k)/2+1)).
%F A116915 G.f.: Product_{k>0} (1-x^(5k))(1-x^(5k-1))(1-x^(5k-4))/((1-x^(5k-2))(1-x^(5k-3))).
%o A116915 (PARI) {a(n)=n=5*n+2; if(issquare(24*n+1,&n), -kronecker(12,n))}
%o A116915 (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^((k%5==0)+ kronecker(5,
               k)), 1+x*O(x^n)), n))}
%Y A116915 Cf. A010815(5n+2)=-a(n).
%Y A116915 Sequence in context: A071003 A071002 A113431 this_sequence A076141 A011751 
               A093709
%Y A116915 Adjacent sequences: A116912 A116913 A116914 this_sequence A116916 A116917 
               A116918
%K A116915 sign
%O A116915 0,1
%A A116915 Michael Somos, Feb 26 2006

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