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.

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

Author

Ran Pan, Nov 16 2015

Keywords

• nonn
• tabl

Comments

Elements in each row are increasing.

Examples

			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;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

Cf. A000007, A000169, A000272, A000918, A291121.

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

Extensions

Edited by Alois P. Heinz, Nov 26 2015