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%I #17 Mar 04 2020 13:53:17
%S 1,384,187344,16869888,397468752,4631235840,34415333568,187483505664,
%T 814912215120,2975507849088,9486506786400,27053151211008,
%U 70486094556864,169930873475328,384163740664704
%N Theta series of Niemeier lattice of type A_15 D_9.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H G. C. Greubel, <a href="/A008692/b008692.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of (29*E_4(z)^3 + 7*E_6(z)^2)/36. 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 = 29/36 E4[q]^3 + 7/36 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, A008690, A008691, A008693 - A008704.
%K nonn
%O 0,2
%A _N. J. A. Sloane_