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A225688 E.g.f.: sec(x)^3+(sec(x)^2*tan(x)). 2
1, 1, 3, 8, 33, 136, 723, 3968, 25953, 176896, 1376643, 11184128, 101031873, 951878656, 9795436563, 104932671488, 1212135593793, 14544442556416, 186388033956483, 2475749026562048, 34859622790687713, 507711943253426176, 7791941518975112403, 123460740095103991808 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

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

MATHEMATICA

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

CROSSREFS

Cf. A000111, A225689.

Sequence in context: A148917 A120892 A195499 * A109655 A184255 A001120

Adjacent sequences:  A225685 A225686 A225687 * A225689 A225690 A225691

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 26 2013

STATUS

approved

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Last modified August 23 13:58 EDT 2019. Contains 326229 sequences. (Running on oeis4.)