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%I #17 Mar 04 2020 13:48:00
%S 1,312,189072,16851744,397574736,4630888080,34415769024,187484711232,
%T 814906132560,2975516031384,9486515132640,27053112718944,
%U 70486121264832,169930915072464,384163711731072
%N Theta series of Niemeier lattice of type A_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="/A008694/b008694.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of (55*E_4(z)^3 + 17*E_6(z)^2)/72. - _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 = 55/72 E4[q]^3 + 17/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017 *)
%Y Cf. A004009, A013973.
%Y Cf. A008688 - A008693, A008695 - A008704.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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