|
| |
|
|
A059593
|
|
Number of degree-n permutations of order exactly 5.
|
|
1
| |
|
|
0, 0, 0, 0, 0, 24, 144, 504, 1344, 3024, 78624, 809424, 4809024, 20787624, 72696624, 1961583624, 28478346624, 238536558624, 1425925698624, 6764765838624, 189239120970624, 3500701266525624, 37764092547420624, 288099608198025624
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,6
|
|
|
COMMENTS
| The number of degree-n permutations of order exactly p (where p is prime) satisfies a(n) =a(n-1)+(1+a(n-p))*(n-1)!/(n-p)! with a(n)=0 if p>n. Also a(n)=Sum_{j=1 to floor[n/p]}[n!/(j!*(n-p*j)!*(p^j))].
|
|
|
FORMULA
| a(n) = a(n - 1) + (1 + a(n - 5))*(n - 1)(n - 2)(n - 3)(n - 4) = Sum_{j = 1 to floor[n/5]}[n!/(j!*(n - 5j)!*(5^j))].
|
|
|
CROSSREFS
| Cf. A001471.
Sequence in context: A076835 A007900 A158874 * A200194 A054118 A001342
Adjacent sequences: A059590 A059591 A059592 * A059594 A059595 A059596
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jan 26 2001
|
| |
|
|
