%I A082564
%S A082564 1,2,2,4,2,0,4,0,2,6,0,4,4,0,0,0,2,4,6,4,0,0,4,0,4,2,0,8,0,0,0,0,2,8,4,
%T A082564 0,6,0,4,0,0,4,0,4,4,0,0,0,4,2,2,8,0,0,8,0,0,8,0,4,0,0,0,0,2,0,8,4,4,0,
%U A082564 0,0,6,4,0,4,4,0,0,0,0,10,4,4,0,0,4,0,4,4,0,0,0,0,0,0,4,4,2,12,2,0,8,0
%V A082564 1,-2,-2,4,2,0,-4,0,2,-6,0,4,4,0,0,0,2,-4,-6,4,0,0,-4,0,4,-2,0,8,0,0,0,
               0,2,-8,-4,0,6,0,
%W A082564 -4,0,0,-4,0,4,4,0,0,0,4,-2,-2,8,0,0,-8,0,0,-8,0,4,0,0,0,0,2,0,-8,4,4,
               0,0,0,6,-4,0,4,4,
%X A082564 0,0,0,0,-10,-4,4,0,0,-4,0,4,-4,0,0,0,0,0,0,4,-4,-2,12,2,0,-8,0
%N A082564 Expansion of eta(q)^2* eta(q^2)/ eta(q^4) in powers of q.
%C A082564 Absolute values appear to give A033715=2*A002325.
%F A082564 Expansion of phi(-q)*phi(-q^2) in powers of q where phi() is a Ramanujan 
               theta function.
%F A082564 Euler transform of period 4 sequence [ -2, -3, -2, -2, ...]. - Michael 
               Somos Mar 30 2007
%F A082564 G.f.: Product_{k>0} (1-x^k)^2/ (1+x^(2k)) .
%o A082564 (PARI) {a(n)= if(n<1, n==0, 2*(-1)^((n+1)\2)* sumdiv(n, d, kronecker(-8, 
               d)))} /* Michael Somos Mar 30 2007 */
%o A082564 (PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)^2* 
               eta(x^2+A)/ eta(x^4+A), n))}
%Y A082564 -2*A129134(n)= a(n) if n>0.
%Y A082564 Sequence in context: A129355 A080963 A033715 this_sequence A133692 A139093 
               A080918
%Y A082564 Adjacent sequences: A082561 A082562 A082563 this_sequence A082565 A082566 
               A082567
%K A082564 sign
%O A082564 0,2
%A A082564 Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2003