cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A008691 Theta series of Niemeier lattice of type A_17 E_7.

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%I A008691 #30 Sep 11 2022 09:33:27
%S A008691 1,432,186192,16881984,397398096,4631467680,34415043264,187482701952,
%T A008691 814916270160,2975502394224,9486501222240,27053176872384,
%U A008691 70486076751552,169930845743904,384163759953792,820167146628480,1668890516764752,3249628128869472,6096883839494544
%N A008691 Theta series of Niemeier lattice of type A_17 E_7.
%C A008691 Also the theta series for the Niemeier lattice of type D_10 E_7^2. - clarified by _Ben Mares_, Jul 17 2022
%D A008691 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.
%H A008691 G. C. Greubel, <a href="/A008691/b008691.txt">Table of n, a(n) for n = 0..1000</a>
%F A008691 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 A008691 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 A008691 Cf. A004009, A013973.
%K A008691 nonn
%O A008691 0,2
%A A008691 _N. J. A. Sloane_
%E A008691 More terms from _Sean A. Irvine_, Mar 22 2020