OFFSET
1,3
COMMENTS
T(n,k) is the number of permutations p of [n] such that p(i)<p(i+k) for i in [n-k]. T(4,2) = 6: 1234, 1243, 1324, 2134, 2143, 3142. - Alois P. Heinz, Feb 09 2023
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..5000
EXAMPLE
First seven rows:
1
1 2
1 3 6
1 6 12 24
1 10 30 60 120
1 20 90 180 360 720
1 35 210 630 1260 2520 5040
...
Writing floor as [ ], the numbers comprising row 4 are
T(4,1) = 4!/[4/1]! = 24/24 = 1
T(4,2) = 4!/([4/2]![5/2]!) = 24/(2*2) = 6
T(4,3) = 4!/([4/3]![5/3]![6/3]! = 24/(1*1*2) = 12
T(4,4) = 4!/([4/4]![5/4]![6/4]![7/4]!) = 24/(1*1*1*1) = 24.
MAPLE
T:= (n, k)-> combinat[multinomial](n, floor((n+i)/k)$i=0..k-1):
seq(seq(T(n, k), k=1..n), n=1..10); # Alois P. Heinz, Feb 09 2023
MATHEMATICA
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 11 2014
STATUS
approved