

A008662


Theta series of direct sum of 6 copies of D_4 lattice.


1



1, 144, 8784, 294336, 5883984, 71916768, 547468992, 2882049408, 12927121488, 45761350608, 150532923744, 416276152128, 1118182645440, 2614241349216, 6094718050176, 12618123283584, 26478496036944
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OFFSET

0,2


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, p. 119.


LINKS



EXAMPLE

G.f. = 1 + 144*q + 8784*q^2 + 294336*q^3 + 5883984*q^4 + 71916768*q^5 + ...  Michael Somos, May 27 2022


MATHEMATICA

terms = 17; s = (1/2 (EllipticTheta[3, 0, q]^4 + EllipticTheta[4, 0, q]^4) )^6 + O[q]^(2 terms); CoefficientList[s, q^2] (* JeanFrançois Alcover, Jul 08 2017 *)
a[ n_] := With[{e1 = q*QPochhammer[q]^24, e2 = q^2*QPochhammer[q^2]^24}, SeriesCoefficient[(e1 + 64* e2)^3 / (e1* e2), {q, 0, n}]]; (* Michael Somos, May 27 2022 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



