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 A302863 #9 Feb 16 2025 08:33:53
%S A302863 1,2,6,29,165,1203,9763,83877,793049,7903501,83570177,933697153,
%T A302863 10905583809,133352809334,1695473999478,22354920990148,
%U A302863 305096197935075,4296142551821184,62336908825014452,930284705538262688,14255992611680074754,224065160215526683317,3607018540134004189466
%N A302863 a(n) = [x^(n^2)] (1 + theta_3(x))^n/(2^n*(1 - x)), where theta_3() is the Jacobi theta function.
%C A302863 a(n) = number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_n)^2 <= n^2.
%H A302863 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>
%H A302863 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%t A302863 Table[SeriesCoefficient[(1 + EllipticTheta[3, 0, x])^n/(2^n (1 - x)), {x, 0, n^2}], {n, 0, 22}]
%t A302863 Table[SeriesCoefficient[1/(1 - x) Sum[x^k^2, {k, 0, n}]^n, {x, 0, n^2}], {n, 0, 22}]
%Y A302863 Main diagonal of A302998.
%Y A302863 Cf. A000603, A000604, A010052, A055403, A055404, A055405, A055406, A055407, A055408, A055409, A298329, A302861, A302862.
%K A302863 nonn
%O A302863 0,2
%A A302863 _Ilya Gutkovskiy_, Apr 14 2018