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

0,4

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.

Links

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

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

Example

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).

Mathematica

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

Crossrefs

Sequence in context: A353779 A088994 A330505 * A141598 A071599 A047695

Adjacent sequences: A214846 A214847 A214848 * A214850 A214851 A214852

Keyword

nonn

Author

Geoffrey Critzer, Mar 08 2013

Status

approved