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.

A004409 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-8).

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%I A004409 #21 Sep 20 2018 09:17:25
%S A004409 1,-16,144,-960,5264,-25056,106944,-418176,1520784,-5201232,16871648,
%T A004409 -52252992,155341248,-445226848,1234726272,-3323392128,8704504976,
%U A004409 -22234655520,55498917840,-135595345600,324759439584
%N A004409 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-8).
%H A004409 Seiichi Manyama, <a href="/A004409/b004409.txt">Table of n, a(n) for n = 0..10000</a>
%F A004409 a(n) ~ (-1)^n * exp(2*Pi*sqrt(2*n)) / (64*2^(3/4)*n^(11/4)). - _Vaclav Kotesovec_, Aug 18 2015
%F A004409 From _Ilya Gutkovskiy_, Sep 20 2018: (Start)
%F A004409 G.f.: 1/theta_3(x)^8, where theta_3() is the Jacobi theta function.
%F A004409 G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^8. (End)
%t A004409 nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^8, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%o A004409 (PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^8) \\ _Altug Alkan_, Sep 20 2018
%Y A004409 Cf. A000122, A000143.
%K A004409 sign
%O A004409 0,2
%A A004409 _N. J. A. Sloane_