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A055379
16*a(n) gives theta series of the shadow of the 24-dimensional odd Leech lattice.
1
3, 12216, 1049332, 24866496, 289421466, 2150562080, 11720932296, 50917793280, 186017041471, 592764490128, 1691223619836, 4404312868096, 10623285300642, 24004367672640, 51272935258008, 104280162643968, 203151521341206
OFFSET
1,1
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.
LINKS
G. Nebe and N. J. A. Sloane, Home page for odd Leech lattice
E. M. Rains and N. J. A. Sloane, The Shadow Theory of Modular and Unimodular Lattices, J. Number Theory, 73 (1998), 359-389.
FORMULA
G.f.: (1/16)*( theta2(z)^24 + 3*theta4(2*z)^8 * theta2(z)^16 + (3/16)*theta4(2*z)^16 * theta2(z)^8 ).
MATHEMATICA
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 *)
CROSSREFS
Cf. A027859.
Sequence in context: A280655 A262651 A309246 * A047777 A195834 A124393
KEYWORD
nonn
AUTHOR
Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 22 2000
STATUS
approved