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A260693
Triangle read by rows: T(n,k) is the number of parking functions of length n whose maximum element is k, where n >= 0 and 0 <= k <= n.
3
1, 0, 1, 0, 1, 2, 0, 1, 6, 9, 0, 1, 14, 46, 64, 0, 1, 30, 175, 465, 625, 0, 1, 62, 596, 2471, 5901, 7776, 0, 1, 126, 1925, 11634, 40376, 90433, 117649, 0, 1, 254, 6042, 51570, 243454, 757940, 1626556, 2097152, 0, 1, 510, 18651, 220887, 1376715, 5580021, 16146957, 33609537, 43046721
OFFSET
0,6
COMMENTS
Elements in each row are increasing.
LINKS
FORMULA
T(n,0) = A000007(n).
T(n,1) = 1 for n>0.
T(n,2) = 2^n - 2 = A000918(n).
T(n,n) = n^(n-1) = A000169(n) for n>0.
Sum of n-th row is A000272(n+1).
T(2n,n) = A291121(n). - Alois P. Heinz, Aug 17 2017
EXAMPLE
For example, T(3,2) = 6 because there are six parking functions of length 3 whose maximum element is 2, namely (1,1,2), (1,2,1), (2,1,1), (1,2,2), (2,1,2), (2,2,1).
Triangle starts:
1;
0, 1;
0, 1, 2;
0, 1, 6, 9;
0, 1, 14, 46, 64;
0, 1, 30, 175, 465, 625;
0, 1, 62, 596, 2471, 5901, 7776;
0, 1, 126, 1925, 11634, 40376, 90433, 117649;
0, 1, 254, 6042, 51570, 243454, 757940, 1626556, 2097152;
0, 1, 510, 18651, 220887, 1376715, 5580021, 16146957, 33609537, 43046721;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ran Pan, Nov 16 2015
EXTENSIONS
Edited by Alois P. Heinz, Nov 26 2015
STATUS
approved