A199495 Number of permutations of [n] starting and ending with an odd number.

0, 1, 0, 2, 4, 36, 144, 1440, 8640, 100800, 806400, 10886400, 108864000, 1676505600, 20118067200, 348713164800, 4881984307200, 94152554496000, 1506440871936000, 32011868528640000, 576213633515520000, 13380961044971520000, 267619220899430400000

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

From Alois P. Heinz, Nov 07 2011: (Start)

a(n) = 2*(n-2)! * [x^(n-2)] x/((1+x)^2*(1-x)^3) for n>=2, else a(n) = n.

a(n) = 2*A152887(n-2) for n>=2, else a(n) = n. (End)

Maple

a:= n-> `if`(n<2, n, ceil(n/2)*(ceil(n/2)-1)*(n-2)!):
seq(a(n), n=0..30); # Alois P. Heinz, Nov 07 2011

Crossrefs

Cf. A052618, A077611, A152887.

Sequence in context: A009090 A009295 A277091 * A182965 A189002 A304558

Adjacent sequences: A199492 A199493 A199494 * A199496 A199497 A199498

Keyword

nonn

Author

Olivier Gérard, Nov 07 2011

Status

approved