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 A023919 Theta series of A*_7 lattice. Expansion of F_8(q^2). 3
 1, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 56, 0, 0, 112, 126, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 576, 0, 0, 672, 756, 0, 0, 0, 0, 0, 0, 1232, 0, 0, 0, 0, 1512, 0, 0, 2016, 2072, 0, 0, 0, 0, 0, 0, 2800, 0, 0, 0, 0, 4032, 0, 0, 4048, 4158, 0, 0, 0, 0, 0, 0, 5712, 0, 0, 0, 0, 5544, 0, 0, 6944, 7560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 REFERENCES S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function. Proc. Amer. Math. Soc. 128 (2000), 1333-1338. J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114. LINKS G. Nebe and N. J. A. Sloane, Home page for this lattice EXAMPLE 1 + 16*q^7 + 56*q^12 + 112*q^15 + 126*q^16 + 336*q^23 + 576*q^28 + 672*q^31 + 756*q^32 + 1232*q^39 + 1512*q^44 + 2016*q^47 + 2072*q^48 + O(q^49) MATHEMATICA terms = 81; phi[q_] := EllipticTheta[3, 0, q]; psi[q_] := (1/2)*q^(-1/8) * EllipticTheta[2, 0, q^(1/2)]; F8[q_] := (1/8) (phi[q^2]^7 + (2 Sqrt[q] psi[q^4])^7 + 14 phi[q^2]^5 phi[q]^2 - 7 phi[q^2]^3 phi[q]^4); s = Simplify[Normal[F8[q^2] + O[q]^terms], q>0]; CoefficientList[s, q][[1 ;; terms]] (* Jean-François Alcover, Jul 04 2017 *) PROG (MAGMA) L:=Lattice("A", 7); D:=Dual(L); T1 := ThetaSeries(D, 60); CROSSREFS Cf. A008447 (A_7). Sequence in context: A111413 A181029 A072838 * A169767 A225611 A173293 Adjacent sequences:  A023916 A023917 A023918 * A023920 A023921 A023922 KEYWORD nonn AUTHOR STATUS approved

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