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 A225689 #18 Aug 05 2019 01:29:28
%S A225689 0,1,2,8,28,136,662,3968,24568,176896,1326122,11184128,98329108,
%T A225689 951878656,9596075582,104932671488,1192744081648,14544442556416,
%U A225689 183983154281042,2475749026562048,34489251602450188,507711943253426176,7722592644581974502,123460740095103991808,2035778987564783402728
%N A225689 E.g.f.: sec(x)^2*tan(x)+sec(x)*tan(x)^2.
%C A225689 Number of up-down max-min permutations of n elements.
%H A225689 Vincenzo Librandi, <a href="/A225689/b225689.txt">Table of n, a(n) for n = 0..200</a>
%H A225689 F. Heneghan and T. K. Petersen, <a href="http://math.depaul.edu/tpeter21/MaxMinUpDownCMJ2v.pdf">Power series for up-down min-max permutations</a>, 2013.
%H A225689 Masato Kobayashi, <a href="https://arxiv.org/abs/1908.00701">A new refinement of Euler numbers on counting alternating permutations</a>, arXiv:1908.00701 [math.CO], 2019.
%F A225689 The e.g.f. can also be written as sin(x)*(1+sin(x))/cos(x)^3.
%F A225689 A225688(n)+a(n) = A000111(n+2). - corrected by _Vaclav Kotesovec_, May 26 2013
%F A225689 a(n) ~ n! * n^2*(2/Pi)^(n+3). - _Vaclav Kotesovec_, May 26 2013
%t A225689 Table[n!*SeriesCoefficient[Sin[x]*(1+Sin[x])/Cos[x]^3,{x,0,n}] ,{n,0,20}] (* _Vaclav Kotesovec_, May 26 2013 *)
%Y A225689 Cf. A000111, A225688.
%K A225689 nonn
%O A225689 0,3
%A A225689 _N. J. A. Sloane_, May 26 2013