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.

A004408 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-7).

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%I A004408 #21 Sep 20 2018 09:17:19
%S A004408 1,-14,112,-672,3346,-14560,57120,-206208,694960,-2209774,6683040,
%T A004408 -19345760,53874912,-144936288,377965760,-958231680,2367566866,
%U A004408 -5713057728,13488657168,-31210552800,70873262880,-158145658560
%N A004408 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-7).
%H A004408 Seiichi Manyama, <a href="/A004408/b004408.txt">Table of n, a(n) for n = 0..10000</a>
%F A004408 a(n) ~ (-1)^n * 49*exp(Pi*sqrt(7*n)) / (4096*n^(5/2)). - _Vaclav Kotesovec_, Aug 18 2015
%F A004408 From _Ilya Gutkovskiy_, Sep 20 2018: (Start)
%F A004408 G.f.: 1/theta_3(x)^7, where theta_3() is the Jacobi theta function.
%F A004408 G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^7. (End)
%t A004408 nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^7, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%o A004408 (PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^7) \\ _Altug Alkan_, Sep 20 2018
%Y A004408 Cf. A000122, A008451.
%K A004408 sign
%O A004408 0,2
%A A004408 _N. J. A. Sloane_