A004406 - OEIS

%I #24 Oct 26 2023 00:19:59

%S 1,-10,60,-280,1110,-3912,12600,-37760,106620,-286290,736184,-1822920,

%T 4365800,-10149320,22971120,-50744448,109643350,-232145040,482403060,

%U -985229640,1980034104,-3920000400,7652388280,-14742829440

%N Expansion of 1 / (Sum_{n=-oo..oo} x^(n^2))^5.

%H Seiichi Manyama, <a href="/A004406/b004406.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (-1)^n * 5^(3/2)*exp(Pi*sqrt(5*n)) / (512*n^2). - _Vaclav Kotesovec_, Aug 18 2015

%F From _Ilya Gutkovskiy_, Sep 20 2018: (Start)

%F G.f.: 1/theta_3(x)^5, where theta_3() is the Jacobi theta function.

%F G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^5. (End)

%t nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^5, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 18 2015 *)

%Y Cf. A000122, A000132.

%K sign

%O 0,2

%A _N. J. A. Sloane_