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%I #30 Sep 11 2022 09:33:27
%S 1,432,186192,16881984,397398096,4631467680,34415043264,187482701952,
%T 814916270160,2975502394224,9486501222240,27053176872384,
%U 70486076751552,169930845743904,384163759953792,820167146628480,1668890516764752,3249628128869472,6096883839494544
%N Theta series of Niemeier lattice of type A_17 E_7.
%C Also the theta series for the Niemeier lattice of type D_10 E_7^2. - clarified by _Ben Mares_, Jul 17 2022
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H G. C. Greubel, <a href="/A008691/b008691.txt">Table of n, a(n) for n = 0..1000</a>
%F This series is the q-expansion of 5/6 E_4(z)^3 + 1/6 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 = 5/6 E4[q]^3 + 1/6 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.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Mar 22 2020
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