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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.

A307901 Expansion of 1/(1 - x * theta_4(x)), where theta_4() is the Jacobi theta function.

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%I A307901 #19 Feb 16 2025 08:33:55
%S A307901 1,1,-1,-3,-1,7,11,-5,-33,-25,53,123,9,-297,-363,323,1273,657,-2415,
%T A307901 -4407,957,12069,11465,-16887,-47915,-12939,104431,152029,-85529,
%U A307901 -476579,-333905,803237,1752799,11597,-4349949,-5019855,5068735,18311655,8392559,-35953969
%N A307901 Expansion of 1/(1 - x * theta_4(x)), where theta_4() is the Jacobi theta function.
%H A307901 Robert Israel, <a href="/A307901/b307901.txt">Table of n, a(n) for n = 0..5045</a>
%H A307901 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%F A307901 G.f.: Sum_{k>=0} x^k * theta_4(x)^k.
%F A307901 G.f.: 1/(1 - x * Sum_{k=-oo..oo} (-1)^k * x^(k^2)).
%F A307901 G.f.: 1/(1 - x * Product_{k>=1} (1 - x^k)/(1 + x^k)).
%p A307901 S:= series(1/(1-x*JacobiTheta4(0,x)),x,101):
%p A307901 seq(coeff(S,x,j),j=0..100);  # _Robert Israel_, Nov 03 2019
%t A307901 nmax = 39; CoefficientList[Series[1/(1 - x EllipticTheta[4, 0, x]), {x, 0, nmax}], x]
%t A307901 nmax = 39; CoefficientList[Series[1/(1 - x Product[(1 - x^k)/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A307901 Cf. A002448, A015128, A032803, A299108.
%K A307901 sign
%O A307901 0,4
%A A307901 _Ilya Gutkovskiy_, May 04 2019