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%I #21 Mar 04 2020 01:48:47
%S 1,528,183888,16906176,397256784,4631931360,34414462656,187481094528,
%T 814924380240,2975491484496,9486490093920,27053228195136,
%U 70486041140928,169930790281056,384163798531968
%N Theta series of Niemeier lattice of type D_12^2.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H G. C. Greubel, <a href="/A008690/b008690.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of 8/9 E_4(z)^3 + 1/9 E_6(z)^2. See A004009 and A013973. - _Daniel D. Briggs_, Nov 25 2011
%t terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 8/9 E4[q]^3 + 1/9 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y Cf. A008688, A008689, A008691 - A008704.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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