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Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-21).
1

%I #14 Jun 24 2017 05:10:34

%S 1,-42,924,-14168,169974,-1698312,14692216,-112987776,787175004,

%T -5039316786,29971442424,-167060546184,878920016296,-4390113366408,

%U 20920981191792,-95515527307648,419275600889334,-1775001330567696

%N Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-21).

%H Seiichi Manyama, <a href="/A004422/b004422.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 21 for this sequence. - _Vaclav Kotesovec_, Aug 18 2015

%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^21, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_