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A008696 Theta series of Niemeier lattice of type D_6^4. 5

%I

%S 1,240,190800,16833600,397680720,4630540320,34416204480,187485916800,

%T 814900050000,2975524213680,9486523478880,27053074226880,

%U 70486147972800,169930956669600,384163682797440,820166912933760

%N Theta series of Niemeier lattice of type D_6^4.

%C Also the theta series for A_9^2*D_6.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

%H G. C. Greubel, <a href="/A008696/b008696.txt">Table of n, a(n) for n = 0..1000</a>

%F This series is the q-expansion of (13*E_4(z)^3 + 5*E_6(z)^2)/18. - _Daniel D. Briggs_, Nov 25 2011

%t terms = 15; th = EllipticTheta; E4 = 1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}] + O[q]^terms; E6 = th[2, 0, q]^12 + th[3, 0, q]^12 - 33*th[2, 0, q]^4*th[3, 0, q]^4*(th[2, 0, q]^4 + th[3, 0, q]^4); CoefficientList[ (13/18)*E4^3 + (5/18)*E6^2 + O[q]^terms, q] (* _Jean-Fran├žois Alcover_, Jul 05 2017 *)

%Y Cf. A004009, A013973.

%Y Cf. A008688 - A008695, A008697 - A008704.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

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Last modified July 27 17:35 EDT 2021. Contains 346308 sequences. (Running on oeis4.)