%I #9 Mar 16 2022 02:55:07

%S 3,12216,1049332,24866496,289421466,2150562080,11720932296,

%T 50917793280,186017041471,592764490128,1691223619836,4404312868096,

%U 10623285300642,24004367672640,51272935258008,104280162643968,203151521341206

%N 16*a(n) gives theta series of the shadow of the 24-dimensional odd Leech lattice.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.

%H G. C. Greubel, <a href="/A055379/b055379.txt">Table of n, a(n) for n = 1..1000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/oddLeech.html">Home page for odd Leech lattice</a>

%H E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/shad.html">The Shadow Theory of Modular and Unimodular Lattices</a>, J. Number Theory, 73 (1998), 359-389.

%F G.f.: (1/16)*( theta2(z)^24 + 3*theta4(2*z)^8 * theta2(z)^16 + (3/16)*theta4(2*z)^16 * theta2(z)^8 ).

%t CoefficientList[Series[(EllipticTheta[2, 0, q^(1/2)]^24 + 3*EllipticTheta[2, 0, q^(1/2)]^16*EllipticTheta[4, 0, q]^8 + (3/16)*EllipticTheta[2, 0, q^(1/2)]^8*EllipticTheta[4, 0, q]^16)/16, {q, 0, 30}], q] (* _G. C. Greubel_, Mar 15 2022 *)

%Y Cf. A027859.

%K nonn

%O 1,1

%A Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 22 2000