A225689 E.g.f.: sec(x)^2*tan(x)+sec(x)*tan(x)^2.

0, 1, 2, 8, 28, 136, 662, 3968, 24568, 176896, 1326122, 11184128, 98329108, 951878656, 9596075582, 104932671488, 1192744081648, 14544442556416, 183983154281042, 2475749026562048, 34489251602450188, 507711943253426176, 7722592644581974502, 123460740095103991808, 2035778987564783402728

Offset: 0

Author

N. J. A. Sloane, May 26 2013

Keywords

• nonn

Comments

Number of up-down max-min 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, A225688.

Programs

Mathematica

Table[n!*SeriesCoefficient[Sin[x]*(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 sin(x)*(1+sin(x))/cos(x)^3.

A225688(n)+a(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