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.

A004414 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-13).

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%I A004414 #17 Sep 20 2018 08:44:42
%S A004414 1,-26,364,-3640,29094,-197288,1177176,-6333184,31258604,-143374530,
%T A004414 617193304,-2513060264,9739727816,-36115518376,128680223152,
%U A004414 -442158402816,1469734751654,-4738671343952,14853923411652
%N A004414 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-13).
%H A004414 Seiichi Manyama, <a href="/A004414/b004414.txt">Table of n, a(n) for n = 0..10000</a>
%F A004414 a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 13 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015
%F A004414 From _Ilya Gutkovskiy_, Sep 20 2018: (Start)
%F A004414 G.f.: 1/theta_3(x)^13, where theta_3() is the Jacobi theta function.
%F A004414 G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^13. (End)
%t A004414 nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^13, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%Y A004414 Cf. A000122, A276285.
%K A004414 sign
%O A004414 0,2
%A A004414 _N. J. A. Sloane_