Search: id:A093068
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%I A093068
%S A093068 1,1,2,1,3,3,4,3,5,6,9,8,11,12,15,16,18,21,26,28,35,39,47,51,58,66,77,
%T A093068 85,97,108,125,141,156,174,195,218,245,270,304,336,377,417,467,512,573,
%U A093068 627,702,770,853,935,1035,1136,1257,1371,1515,1654,1822,1989,2184,2382
%N A093068 Expansion of (eta(q^3)^2eta(q^7)eta(q^63))/(eta(q)eta(q^9)eta(q^21)^2) 
               in powers of q.
%C A093068 Euler transform of period 63 sequence [1,1,-1,1,1,-1,0,1,0,1,1,-1,1,0,
               -1,1,1,0,1,1,0,1,1,-1,1,1,0,0,1,-1,1,1,-1,1,0,0,1,1,-1,1,1,0,1,1,
               0,1,1,-1,0,1,-1,1,1,0,1,0,-1,1,1,-1,1,1,0,...].
%F A093068 G.f. A(x) satisfies 0=f(A(x), A(x^2))=f(1/A(x), 1/A(x^2)) where f(u, 
               v)=u^3+v^3-2uv(u+v)-u^2v^2-uv.
%F A093068 G.f.: x Product_{k>0} ((1-x^(3k))^2(1-x^(7k))(1-x^(63k))/(1-x^k)(1-x^(9k))(1-x^(21k))^2).
%o A093068 (PARI) a(n)=local(A,u,v); if(n<0,0,A=x; for(k=2,n,u=A+x*O(x^k); v=subst(u,
               x,x^2); A-=x^k*polcoeff(u^3+v^3-2*u*v*(u+v)-u^2*v^2-u*v,k+2)/2); 
               polcoeff(A,n))
%o A093068 (PARI) a(n)=local(A); if(n<1,0,n--; A=x*O(x^n); polcoeff(eta(x^3+A)^2*eta(x^7+A)*eta(x^63+A)/
               eta(x+A)/eta(x^9+A)/eta(x^21+A)^2,n))
%Y A093068 Sequence in context: A116087 A163281 A116921 this_sequence A097357 A123621 
               A151662
%Y A093068 Adjacent sequences: A093065 A093066 A093067 this_sequence A093069 A093070 
               A093071
%K A093068 nonn
%O A093068 1,3
%A A093068 Michael Somos, Mar 17 2004

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