A262035 Number of permutations of [2n+1] beginning with exactly n ascents.

1, 2, 15, 168, 2520, 47520, 1081080, 28828800, 882161280, 30474662400, 1173274502400, 49819040409600, 2313026876160000, 116576554558464000, 6338850154116480000, 369890550169620480000, 23056510960573009920000, 1529010726859052236800000

Offset: 0

Author

Alois P. Heinz, Sep 08 2015

Keywords

• nonn

Examples

			a(0) = 1: 1.
a(1) = 2: 132, 231.
a(2) = 15: 12435, 12534, 12543, 13425, 13524, 13542, 14523, 14532, 23415, 23514, 23541, 24513, 24531, 34512, 34521.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..365

Crossrefs

Cf. A262033, A262034.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n+1,
      2*(n+1)*(2*n+1)*a(n-1)/(n+2))
    end:
seq(a(n), n=0..20);

Formula

E.g.f.: (1-2*x)/(4*sqrt(1-4*x)*x^2)+(2*x^2-1)/(4*x^2).

a(n) = 2*(n+1)*(2*n+1)*a(n-1)/(n+2) for n>1, a(n) = n+1 for n<=1.

a(n) = (2*n+1)!/(n+1)! - floor((2*n+2)!/((n+1)!*(n+1)*(n+2)*2)).

a(n) = A262033(2n+1) - A262034(2n+1).