%I A005879 M4509
%S A005879 8,32,48,64,104,96,112,192,144,160,256,192,248,320,240,256,384,384,304,
%T A005879 448,336,352,624,384,456,576,432,576,640,480,496,832,672,544,768,576,
%U A005879 592,992,768,640,968,672,864,960,720,896,1024,960,784,1248,816,832,1536
%N A005879 Theta series of D_4 lattice with respect to deep hole.
%C A005879 Expansion of Jacobi theta_2(q)^4/(2q) in powers of q^2. - Michael Somos 
               Apr 11 2004
%C A005879 Expansion of q^(-1/2)8(eta(q^2)^2/eta(q))^4 in powers of q. - Michael 
               Somos Apr 11 2004
%D A005879 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005879 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", 
               Springer-Verlag, p. 118.
%H A005879 T. D. Noe, <a href="b005879.txt">Table of n, a(n) for n=0..10000</a>
%H A005879 G. Nebe and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               lattices/D4.html">Home page for this lattice</a>
%H A005879 <a href="Sindx_Da.html#D4">Index entries for sequences related to D_4 
               lattice</a>
%F A005879 G.f.: 8(Product_{k>0} (1-x^k)(1+x^k)^2)^4. - Michael Somos Apr 11 2004
%o A005879 (PARI) a(n)=if(n<0,0,8*sigma(2*n+1))
%Y A005879 A008438(n)=a(n)/8. A005880(n)=a(n)/4. A000118(2n+1)=-A096727(2n+1)=a(n).
%Y A005879 Sequence in context: A144096 A127988 A129749 this_sequence A067519 A009245 
               A018842
%Y A005879 Adjacent sequences: A005876 A005877 A005878 this_sequence A005880 A005881 
               A005882
%K A005879 nonn,easy,nice
%O A005879 0,1
%A A005879 N. J. A. Sloane (njas(AT)research.att.com).