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 A291331 #8 Jun 08 2019 11:04:50
%S A291331 1,2,80,152064,31832735744,1278532180456243200,
%T A291331 15158097871912903189326725120,
%U A291331 75553979800594222861911290918096439607296,213679399657239557797941463213636090471439135194537263104
%N A291331 a(n) = [x^n] 1/(1 - 2^n*x/(1 - 4^n*x/(1 - 6^n*x/(1 - 8^n*x/(1 - 10^n*x/(1 - ...)))))), a continued fraction.
%F A291331 a(n) = A291260(n,n).
%F A291331 a(n) ~ c * 2^(n^2) * (n!)^n ~ c * Pi^(n/2) * (2*n)^(n^2 + n/2) / exp(n^2 - 1/12), where c = 1/QPochhammer(exp(-1)) = 1.982440907412873703685682465561312... - _Vaclav Kotesovec_, Jun 08 2019
%t A291331 Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-(2 i)^n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 8}]
%Y A291331 Main diagonal of A291260.
%Y A291331 Cf. A291333.
%K A291331 nonn
%O A291331 0,2
%A A291331 _Ilya Gutkovskiy_, Aug 22 2017