|
Search: id:A145221
|
|
|
| A145221 |
|
a(n) is the number of odd permutations (of an n-set) without a fixed point. Equivalently, it is the number of odd derangements (of an n-set) |
|
+0
6
|
|
| 0, 0, 1, 0, 6, 20, 135, 924, 7420, 66744, 667485, 7342280, 88107426, 1145396460, 16035550531
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
REFERENCES
|
Ali, Bashir and Umar, A., "Some combinatorial properties of the alternating group". Southeast Asian Bulletin Math. 32 (2008), 823-830.
|
|
FORMULA
|
a(n) = (n!/2)sum(i=0, n-2, ((-1)^i)/i!
a(n) = (A000166(n)+(-1^n)(n-1))/2
Egf.: ((x^2)e^(-x))/2(1-x)
|
|
EXAMPLE
|
a(4) = 6 because there are exactly 6 odd permutations (of a 4-set) without a fixed point, namely: (1234), (1243), (1324), (1342), (1423), (1432)
|
|
CROSSREFS
|
A000166
Sequence in context: A074013 A114959 A000386 this_sequence A000387 A027148 A095854
Adjacent sequences: A145218 A145219 A145220 this_sequence A145222 A145223 A145224
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
A. Umar (aumarh(AT)squ.edu.om), Oct 09 2008
|
|
|
Search completed in 0.002 seconds
|
