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.
%I A303333 #12 Feb 16 2025 08:33:54
%S A303333 1,0,4,24,24,560,2080,11088,74864,343536,2050344,11676280,61903776,
%T A303333 363737712,2022013760,11335886864,65187410400,365627715968,
%U A303333 2085523894756,11894205734280,67517852274384,386394626371680,2205027379874400,12602057718873040,72195482578935488,413235574714857360
%N A303333 a(n) = [x^n] (theta_3(x^(1/2))^n + theta_4(x^(1/2))^n)/2, where theta_3() and theta_4() are the Jacobi theta functions.
%H A303333 Seiichi Manyama, <a href="/A303333/b303333.txt">Table of n, a(n) for n = 0..1000</a>
%H A303333 J. H. Conway and N. J. A. Sloane, <a href="http://dx.doi.org/10.1007/978-1-4757-2016-7">Sphere Packings, Lattices and Groups</a>, Springer-Verlag, p. 118.
%H A303333 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%F A303333 a(n) = A297331(n,n).
%F A303333 a(n) ~ c * d^n / sqrt(n), where d = 5.84456473064455581274428417... and c = 0.14104739588693592503498... - _Vaclav Kotesovec_, Jun 26 2019
%t A303333 Table[SeriesCoefficient[(EllipticTheta[3, 0, x^(1/2)]^n + EllipticTheta[4, 0, x^(1/2)]^n)/2, {x, 0, n}], {n, 0, 25}]
%t A303333 Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n, {x, 0, 2 n}], {n, 0, 25}]
%t A303333 Table[SeriesCoefficient[EllipticTheta[3, 0, Sqrt[x]]^n, {x, 0, n}], {n, 0, 25}] (* _Vaclav Kotesovec_, Jun 26 2019 *)
%Y A303333 Main diagonal of A297331.
%Y A303333 Cf. A066535.
%K A303333 nonn
%O A303333 0,3
%A A303333 _Ilya Gutkovskiy_, Apr 21 2018