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 A097593 #11 Jul 04 2019 03:41:43
%S A097593 0,0,1,4,22,138,998,8174,74898,759634,8451862,102381222,1341503546,
%T A097593 18907621562,285259758366,4587192222958,78327809126818,
%U A097593 1415429225667234,26987142531214118,541434621007942454,11402270678456333322
%N A097593 Number of increasing runs of even length in all permutations of [n].
%H A097593 Vincenzo Librandi, <a href="/A097593/b097593.txt">Table of n, a(n) for n = 0..200</a>
%F A097593 E.g.f.: (4*(exp(-x)-1)+4*x-x^2)/(2*(1-x)^2).
%F A097593 a(n) = (2*n-1)*a(n-1) - (n-2)*(n-1)*a(n-2) - (n-2)*(n-1)*a(n-3). - _Vaclav Kotesovec_, Nov 19 2012
%F A097593 a(n) ~ n!*n*(4*exp(-1)-1)/2. - _Vaclav Kotesovec_, Nov 19 2012
%F A097593 a(n) = Sum_{k=1..floor(n/2)} k * A097592(n,k). - _Alois P. Heinz_, Jul 04 2019
%e A097593 Example: a(3)=4 because we have 123,(13)2,2(13),(23)1,3(12),321 (runs of even length shown between parentheses).
%p A097593 G:=(4*(exp(-x)-1)+4*x-x^2)/2/(1-x)^2: Gser:=series(G,x=0,25): 0,seq(n!*coeff(Gser,x^n),n=1..24);
%t A097593 Table[n!*SeriesCoefficient[(4*(E^(-x)-1)+4*x-x^2)/(2*(1-x)^2),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Nov 19 2012 *)
%o A097593 (PARI) x='x+O('x^66); concat([0,0],Vec(serlaplace((4*(exp(-x)-1)+4*x-x^2)/(2*(1-x)^2)))) \\ _Joerg Arndt_, May 11 2013
%Y A097593 Cf. A097592.
%K A097593 nonn
%O A097593 0,4
%A A097593 _Emeric Deutsch_, Aug 29 2004