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.

A108094 Coefficients of series whose 16th power is the theta series of the 16-dimensional Barnes-Wall lattice (see A008409).

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%I A108094 #21 Oct 20 2018 10:23:01
%S A108094 1,0,270,3840,-514080,-15413760,1283087040,62644907520,-3378279124350,
%T A108094 -252933976704000,8502815843769600,1007506223570707200,
%U A108094 -17757117956815481280,-3942183666885514421760,14527133705347401150720,15088544258811557869278720,144818514010649047069497600
%N A108094 Coefficients of series whose 16th power is the theta series of the 16-dimensional Barnes-Wall lattice (see A008409).
%H A108094 Seiichi Manyama, <a href="/A108094/b108094.txt">Table of n, a(n) for n = 0..551</a>
%H A108094 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006.
%H A108094 N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://dx.doi.org/10.1016/j.jcta.2006.03.018">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%e A108094 More precisely, the theta series of the Barnes-Wall lattice begins 1 + 4320*q^2 + 61440*q^3 + 522720*q^4 + 2211840*q^5 + 8960640*q^6 + 23224320*q^7 + ... and the 16th root of this is 1 + 270*q^2 + 3840*q^3 - 514080*q^4 - 15413760*q^5 + 1283087040*q^6 + 62644907520*q^7 - ...
%t A108094 f[q_] := 1/2 (EllipticTheta[2, 0, q]^16 + EllipticTheta[3, 0, q]^16 + EllipticTheta[4, 0, q]^16 + 30 EllipticTheta[2, 0, q]^8 EllipticTheta[3, 0, q]^8);
%t A108094 CoefficientList[f[q]^(1/16) + O[q]^17, q] (* _Jean-François Alcover_, Aug 17 2018 *)
%K A108094 sign
%O A108094 0,3
%A A108094 _N. J. A. Sloane_ and _Michael Somos_, Jun 06 2005