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 A362713 #15 May 05 2023 01:34:27
%S A362713 1,6,256,28560,6071040,2098483200,1071889920000,758870167910400,
%T A362713 711206089850880000,852336059876720640000,1271438437097485762560000,
%U A362713 2310211006286602237378560000,5023141810386294125321256960000,12877606625796048169971744768000000,38439740210093310755176533983232000000
%N A362713 Expansion of e.g.f. x*2F1([3/4, 3/4], [3/2], 4*x^2)/2F1([1/4, 1/4], [1/2], 4*x^2), odd powers only.
%H A362713 Christian Krattenthaler and Thomas W. Müller, <a href="https://arxiv.org/abs/2304.11471">The congruence properties of Romik's sequence of Taylor coefficients of Jacobi's theta function theta_3</a>, arXiv:2304.11471 [math.NT], 2023. See p. 5.
%F A362713 a(n) = Product_{j=1..n} (4*j - 1)^2 - Sum_{m=0..n-1} binomial(2*n+1, 2*m+1)*Product_{j=1..n-m} (4*j - 3)^2*a(m) for n > 0.
%t A362713 Table[(2n+1)!SeriesCoefficient[x*Hypergeometric2F1[3/4, 3/4, 3/2, 4*x^2]/Hypergeometric2F1[1/4, 1/4, 1/2, 4*x^2], {x, 0, 2n+1}], {n,0, 14}]
%t A362713 (* or *)
%t A362713 a[0]=1; a[n_]:=Product[(4j-1)^2,{j,n}]-Sum[Binomial[2n+1,2m+1]Product[(4j-3)^2,{j,n-m}]a[m],{m,0,n-1}]; Array[a,15,0]
%Y A362713 Cf. A317615, A362714, A362715.
%K A362713 nonn
%O A362713 0,2
%A A362713 _Stefano Spezia_, Apr 30 2023