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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

Table of n, a(n) for n=0..80.

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-Fran├žois Alcover, Jul 04 2017 *)

PROG

(MAGMA) L:=Lattice("A", 7); D:=Dual(L); T1<q> := 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

N. J. A. Sloane.

STATUS

approved

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Last modified December 13 14:58 EST 2017. Contains 295958 sequences.