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 A291333 #12 Jul 21 2018 07:23:54
%S A291333 1,1,5,297,485729,38103228225,220579355255364545,
%T A291333 134210828762693919568092033,11583583466188874003924403353591815169,
%U A291333 183988806081826466732185672966967145613350641690625,676960735217941793634104089611911809588055950029181968418342810625
%N A291333 a(n) = [x^n] 1/(1 - x/(1 - 2^n*x/(1 - 3^n*x/(1 - 4^n*x/(1 - 5^n*x/(1 - ...)))))), a continued fraction.
%H A291333 Robert Israel, <a href="/A291333/b291333.txt">Table of n, a(n) for n = 0..30</a>
%F A291333 a(n) = A290569(n,n).
%F A291333 a(n) ~ c * (n!)^n ~ c * 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2-1/12), where c = 1/QPochhammer(exp(-1)) = 1.9824409074128737036856824655613120156828827... - _Vaclav Kotesovec_, Aug 26 2017, updated Jul 21 2018
%p A291333 seq(coeff(series(numtheory:-cfrac([0,[1,1],seq([-i^n*x,1],i=1..n)]),x,n+1),x,n),n=0..15); # _Robert Israel_, Aug 22 2017
%t A291333 Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-i^n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 10}]
%Y A291333 Main diagonal of A290569.
%Y A291333 Cf. A036740.
%K A291333 nonn
%O A291333 0,3
%A A291333 _Ilya Gutkovskiy_, Aug 22 2017