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