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 A331405 #9 Jan 28 2020 06:29:40
%S A331405 1,2,-8,-112,2176,71936,-3163136,-196237312,15258124288,1531746516992,
%T A331405 -185088737017856,-27405687884087296,4747122204712370176,
%U A331405 973473732763710390272,-228670532983871365971968,-62056343388674412796444672,18982531521384459634512756736
%N A331405 G.f.: 1/(1 - 1*2*x/(1 + 2*3*x/(1 - 3*4*x/(1 + 4*5*x/(1 - 5*6*x/(1 + ...)))))), a continued fraction.
%H A331405 Vaclav Kotesovec, <a href="/A331405/b331405.txt">Table of n, a(n) for n = 0..248</a>
%F A331405 a(n) ~ sin((2*n+1)*Pi/4) * 2^(6*n + 8) * Pi^(n + 3/2) * n^(2*n + 3/2) / (exp(2*n) * Gamma(1/4)^(4*n + 4)). - _Vaclav Kotesovec_, Jan 28 2020
%t A331405 nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[(-1)^k k (k + 1) x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A331405 Cf. A000182, A202038.
%K A331405 sign
%O A331405 0,2
%A A331405 _Ilya Gutkovskiy_, Jan 16 2020