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 A225688 #17 Aug 05 2019 01:29:39
%S A225688 1,1,3,8,33,136,723,3968,25953,176896,1376643,11184128,101031873,
%T A225688 951878656,9795436563,104932671488,1212135593793,14544442556416,
%U A225688 186388033956483,2475749026562048,34859622790687713,507711943253426176,7791941518975112403,123460740095103991808
%N A225688 E.g.f.: sec(x)^3+(sec(x)^2*tan(x)).
%C A225688 Number of up-down min-max permutations of n elements.
%H A225688 Vincenzo Librandi, <a href="/A225688/b225688.txt">Table of n, a(n) for n = 0..200</a>
%H A225688 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 A225688 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 A225688 The e.g.f. can also be written as (1+sin(x))/cos(x)^3.
%F A225688 a(n)+A225689(n) = A000111(n+2). - corrected by _Vaclav Kotesovec_, May 26 2013
%F A225688 a(n) ~ n! * n^2*(2/Pi)^(n+3). - _Vaclav Kotesovec_, May 26 2013
%t A225688 Table[n!*SeriesCoefficient[(1+Sin[x])/Cos[x]^3,{x,0,n}] ,{n,0,20}] (* _Vaclav Kotesovec_, May 26 2013 *)
%Y A225688 Cf. A000111, A225689.
%K A225688 nonn
%O A225688 0,3
%A A225688 _N. J. A. Sloane_, May 26 2013