A257546 Number of permutations of length n such that numbers at odd positions are monotone and numbers at even positions are also monotone.

1, 1, 2, 6, 24, 40, 80, 140, 280, 504, 1008, 1848, 3696, 6864, 13728, 25740, 51480, 97240, 194480, 369512, 739024, 1410864, 2821728, 5408312, 10816624, 20801200, 41602400, 80233200, 160466400, 310235040, 620470080, 1202160780, 2404321560, 4667212440

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..2993

Ran Pan, Exercise C, Project P.

Formula

a(n) = 4*binomial(n,floor(n/2))) for n > 4; a(n) = n! for n <= 4.

From Robert Israel, Apr 30 2015: (Start)

G.f.: -3*(1+x)*(1+2*x^2) - 2/x + 2*(2+1/x)/sqrt(1-4*x^2).

a(n+2) = (4*(1+n)*a(n) + 2*a(n+1))/(n+3) for n >= 4. (End)

Maple

f:= gfun:-rectoproc({a(n+2)= 4*(1+n)*a(n)/(n+3) + 2*a(n+1)/(n+3), seq(a(n)=[1, 1, 2, 6, 24, 40, 80][n+1], n=0..5)}, a(n), remember):
map(f, [$0..100]); # Robert Israel, May 12 2015

Mathematica

Table[If[n <= 4, n!, 4 Binomial[n, Floor[n/2]]], {n, 31}] (* Michael De Vlieger, Apr 29 2015 *)

Prog

(Magma) [1, 1, 2, 6] cat [4*Binomial(n, Floor(n/2)): n in [4..40]]; // Vincenzo Librandi, Apr 30 2015

Crossrefs

Cf. A047073, A000142.

Sequence in context: A263690 A137326 A163912 * A274038 A143383 A067653

Adjacent sequences: A257543 A257544 A257545 * A257547 A257548 A257549

Keyword

easy,nonn

Author

Ran Pan, Apr 29 2015

Extensions

More terms from Vincenzo Librandi, Apr 30 2015

Status

approved