Search: id:A129588
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%I A129588
%S A129588 16,64,96,128,208,192,224,384,288,320,512,384,496,640,480,512,768,768,
%T A129588 608,896,672,704,1248,768,912,1152,864,1152,1280,960,992,1664,1344,1088,
%U A129588 1536,1152,1184,1984,1536,1280,1936,1344,1728,1920,1440
%N A129588 Expansion of q^-1 *theta_2(q)^4 in powers of q^2.
%D A129588 K. Bobek, Einleitung in die Theorie der elliptischen Funktionen, Teubner 
               Leipzig, 1884, p. 101.
%F A129588 G.f. sum{n>=0, a(n)*x^(2n+1) } = theta2(q)^4 = theta3(q)^4 - theta4(q)^4.
%F A129588 Expansion of 16*psi(q)^4 in powers of q where psi() is a Ramanujan theta 
               function. - Michael Somos Jun 11 2007
%F A129588 Number of solutions of 2n+1 = (x^2+y^2+z^2+w^2)/4 in odd integers. - 
               Michael Somos Jun 11 2007
%F A129588 G.f.: 16 * (Product_{k>0} (1-x^k)(1+x^k)^2)^4. - Michael Somos Jun 11 
               2007
%o A129588 (PARI) {a(n)= if(n<0, 0, 16*sigma(2*n+1))} /* Michael Somos Jun 11 2007 
               */
%Y A129588 a(n) = 16*A008438(n) = A000118(n)-A096727(n). Cf. A000122, A002448.
%Y A129588 Sequence in context: A062320 A117453 A039370 this_sequence A043193 A043973 
               A153262
%Y A129588 Adjacent sequences: A129585 A129586 A129587 this_sequence A129589 A129590 
               A129591
%K A129588 nonn
%O A129588 0,1
%A A129588 Ralf Stephan (ralf(AT)ark.in-berlin.de), May 30 2007

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