A214849 Number of n-permutations having all cycles of odd length and at most one fixed point.

1, 1, 0, 2, 8, 24, 184, 1000, 8448, 66752, 670976, 6771456, 80540800, 981684352, 13555365888, 193136762624, 3042586824704, 49558509465600, 877951349198848, 16081833643651072, 316609129672114176, 6439690754082062336, 139521103623589068800

Offset: 0

Author

Geoffrey Critzer, Mar 08 2013

Keywords

• nonn

Comments

a(n) is also the number of n-permutations with exactly one square root. Cf. A003483 which counts n-permutations with at least one square root.

Examples

			a(6)= 184 because we have 144 6-permutations of the type (1,2,3,4,5)(6) and 40 of the type (1,2,3)(4,5,6).  These have exactly one square root: (1,4,2,5,3)(6) and (1,3,2)(4,6,5).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Mathematica

nn=22; Range[0,nn]! CoefficientList[Series[(1+x)((1+x)/(1-x))^(1/2) Exp[-x], {x,0,nn}], x]

Formula

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

a(n) ~ 4*n^n/exp(n+1). - Vaclav Kotesovec, Oct 08 2013