|
|
A138770
|
|
Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} such that there are exactly k entries between the entries 1 and 2 (n>=2, 0<=k<=n-2).
|
|
3
|
|
|
2, 4, 2, 12, 8, 4, 48, 36, 24, 12, 240, 192, 144, 96, 48, 1440, 1200, 960, 720, 480, 240, 10080, 8640, 7200, 5760, 4320, 2880, 1440, 80640, 70560, 60480, 50400, 40320, 30240, 20160, 10080, 725760, 645120, 564480, 483840, 403200, 322560, 241920, 161280, 80640
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = 2*(n-k-1)*(n-2)!.
Sum_{k=0..n-2} k*T(n,k) = n!*(n-2)/3 = A090672(n-1).
|
|
EXAMPLE
|
T(4,2)=4 because we have 1342, 1432, 2341 and 2431.
Triangle starts:
2;
4,2;
12,8,4;
48,36,24,12;
240,192,144,96,48;
...
|
|
MAPLE
|
T:=proc(n, k) if n-2 < k then 0 else (2*n-2*k-2)*factorial(n-2) end if end proc; for n from 2 to 10 do seq(T(n, k), k=0..n-2) end do; # yields sequence in triangular form
|
|
MATHEMATICA
|
Table[Table[2 (n - r) (n - 2)!, {r, 1, n - 1}], {n, 1, 10}] // Grid (* Geoffrey Critzer, Dec 19 2009 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|