A225688 E.g.f.: sec(x)^3+(sec(x)^2*tan(x)).

1, 1, 3, 8, 33, 136, 723, 3968, 25953, 176896, 1376643, 11184128, 101031873, 951878656, 9795436563, 104932671488, 1212135593793, 14544442556416, 186388033956483, 2475749026562048, 34859622790687713, 507711943253426176, 7791941518975112403, 123460740095103991808

Offset: 0

Author

N. J. A. Sloane, May 26 2013

Keywords

• nonn

Comments

Number of up-down min-max permutations of n elements.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• F. Heneghan and T. K. Petersen, Power series for up-down min-max permutations, 2013.
• Masato Kobayashi, A new refinement of Euler numbers on counting alternating permutations, arXiv:1908.00701 [math.CO], 2019.

Crossrefs

Cf. A000111, A225689.

Programs

Mathematica

Table[n!*SeriesCoefficient[(1+Sin[x])/Cos[x]^3,{x,0,n}] ,{n,0,20}] (* Vaclav Kotesovec, May 26 2013 *)

Formula

The e.g.f. can also be written as (1+sin(x))/cos(x)^3.

a(n)+A225689(n) = A000111(n+2). - corrected by Vaclav Kotesovec, May 26 2013

a(n) ~ n! * n^2*(2/Pi)^(n+3). - Vaclav Kotesovec, May 26 2013