A307901 - OEIS

%I #18 Nov 03 2019 05:01:26

%S 1,1,-1,-3,-1,7,11,-5,-33,-25,53,123,9,-297,-363,323,1273,657,-2415,

%T -4407,957,12069,11465,-16887,-47915,-12939,104431,152029,-85529,

%U -476579,-333905,803237,1752799,11597,-4349949,-5019855,5068735,18311655,8392559,-35953969

%N Expansion of 1/(1 - x * theta_4(x)), where theta_4() is the Jacobi theta function.

%H Robert Israel, <a href="/A307901/b307901.txt">Table of n, a(n) for n = 0..5045</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>

%F G.f.: Sum_{k>=0} x^k * theta_4(x)^k.

%F G.f.: 1/(1 - x * Sum_{k=-oo..oo} (-1)^k * x^(k^2)).

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

%p S:= series(1/(1-x*JacobiTheta4(0,x)),x,101):

%p seq(coeff(S,x,j),j=0..100);  # _Robert Israel_, Nov 03 2019

%t nmax = 39; CoefficientList[Series[1/(1 - x EllipticTheta[4, 0, x]), {x, 0, nmax}], x]

%t nmax = 39; CoefficientList[Series[1/(1 - x Product[(1 - x^k)/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

%Y Cf. A002448, A015128, A032803, A299108.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, May 04 2019