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.

A004416 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-15).

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%I A004416 #19 Sep 20 2018 09:06:06
%S A004416 1,-30,480,-5440,48930,-371136,2464320,-14688000,80001120,-403533790,
%T A004416 1904433984,-8477603520,35829727680,-144548556480,559157308800,
%U A004416 -2081866609920,7484792950050,-26057409056640,88057506412320
%N A004416 Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-15).
%H A004416 Seiichi Manyama, <a href="/A004416/b004416.txt">Table of n, a(n) for n = 0..10000</a>
%F A004416 a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 15 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015
%F A004416 From _Ilya Gutkovskiy_, Sep 20 2018: (Start)
%F A004416 G.f.: 1/theta_3(x)^15, where theta_3() is the Jacobi theta function.
%F A004416 G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^15. (End)
%t A004416 nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^15, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)
%o A004416 (PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^15) \\ _Altug Alkan_, Sep 20 2018
%Y A004416 Cf. A000122, A276287.
%K A004416 sign
%O A004416 0,2
%A A004416 _N. J. A. Sloane_