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.

A004411 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-10).

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%I A004411 #23 Sep 20 2018 09:17:42
%S A004411 1,-20,220,-1760,11420,-63624,315040,-1418560,5903260,-22976820,
%T A004411 84413912,-294841120,984745120,-3159938760,9780562880,-29296914112,
%U A004411 85169213340,-240882506920,664216884540,-1788966694240,4714033526616,-12170584419840,30826269009760
%N A004411 Expansion of ( Sum_{n = -infinity..infinity} x^(n^2) )^(-10).
%H A004411 Seiichi Manyama, <a href="/A004411/b004411.txt">Table of n, a(n) for n = 0..10000</a>
%F A004411 a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 10 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015
%F A004411 From _Ilya Gutkovskiy_, Sep 20 2018: (Start)
%F A004411 G.f.: 1/theta_3(x)^10, where theta_3() is the Jacobi theta function.
%F A004411 G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^10. (End)
%t A004411 nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^10, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%o A004411 (PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^10) \\ _Altug Alkan_, Sep 20 2018
%Y A004411 Cf. A000122, A000144.
%K A004411 sign
%O A004411 0,2
%A A004411 _N. J. A. Sloane_