|
|
A209290
|
|
Number of elements whose preimage is the empty set summed over all functions f:{1,2,...,n}->{1,2,...,n}.
|
|
2
|
|
|
0, 0, 2, 24, 324, 5120, 93750, 1959552, 46118408, 1207959552, 34867844010, 1100000000000, 37661140520652, 1390911669927936, 55123269399790046, 2333521433367183360, 105094533691406250000, 5017514388048998039552, 253135520137219049838162, 13456471561751415850795008
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(n)/n^n is the expected value of the number of such elements which approaches n/e as n gets large.
a(n) = Sum_{k=1..n} A219859(n,k)*k.
a(n-1) is the number of length-n words of n-1 letters where adjacent letters are distinct, see example. - Joerg Arndt, Jun 10 2013
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n*(n - 1)^n.
|
|
EXAMPLE
|
There are a(4-1)=a(3)=24 length-4 words of 3 letters (0,1,2) where adjacent letters are distinct:
01: [ 0 1 0 1 ]
02: [ 0 1 0 2 ]
03: [ 0 1 2 0 ]
04: [ 0 1 2 1 ]
05: [ 0 2 0 1 ]
06: [ 0 2 0 2 ]
07: [ 0 2 1 0 ]
08: [ 0 2 1 2 ]
09: [ 1 0 1 0 ]
10: [ 1 0 1 2 ]
11: [ 1 0 2 0 ]
12: [ 1 0 2 1 ]
13: [ 1 2 0 1 ]
14: [ 1 2 0 2 ]
15: [ 1 2 1 0 ]
16: [ 1 2 1 2 ]
17: [ 2 0 1 0 ]
18: [ 2 0 1 2 ]
19: [ 2 0 2 0 ]
20: [ 2 0 2 1 ]
21: [ 2 1 0 1 ]
22: [ 2 1 0 2 ]
23: [ 2 1 2 0 ]
24: [ 2 1 2 1 ]
(End)
|
|
MATHEMATICA
|
Table[n (n-1)^n, {n, 0, 20}]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|