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.

A001943 Expansion of reciprocal of theta series of E_8 lattice.

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%I A001943 #16 Mar 05 2018 06:16:28
%S A001943 1,-240,55440,-12793920,2952385680,-681306078240,157221316739520,
%T A001943 -36281112432850560,8372395974330234000,-1932052510261208053680,
%U A001943 445849302141400152457440,-102886230661038692118348480
%N A001943 Expansion of reciprocal of theta series of E_8 lattice.
%D A001943 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 123.
%H A001943 Seiichi Manyama, <a href="/A001943/b001943.txt">Table of n, a(n) for n = 0..422</a>
%F A001943 a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n), where c = 512 * Pi^12 / (9 * Gamma(1/3)^18) = 1.0411095643149212575756525710182812978684243780094495837147096816494... - _Vaclav Kotesovec_, Jul 02 2017, updated Mar 05 2018
%t A001943 terms = 12; s = 1/(1 + 240*Sum[k^3*(q^k/(1 - q^k)), {k, 1, terms}]) + O[q]^terms; CoefficientList[s, q] (* _Jean-François Alcover_, Jul 04 2017 *)
%Y A001943 Cf. A004009.
%K A001943 sign
%O A001943 0,2
%A A001943 _N. J. A. Sloane_