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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. 2

%I

%S 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,

%T 5901,7776,0,1,126,1925,11634,40376,90433,117649,0,1,254,6042,51570,

%U 243454,757940,1626556,2097152,0,1,510,18651,220887,1376715,5580021,16146957,33609537,43046721

%N 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.

%C Elements in each row are increasing.

%H Alois P. Heinz, <a href="/A260693/b260693.txt">Rows n = 0..140, flattened</a>

%F T(n,0) = A000007(n).

%F T(n,1) = 1 for n>0.

%F T(n,2) = 2^n - 2 = A000918(n).

%F T(n,n) = n^(n-1) = A000169(n) for n>0.

%F Sum of n-th row is A000272(n+1).

%F T(2n,n) = A291121(n). - _Alois P. Heinz_, Aug 17 2017

%e 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).

%e Triangle starts:

%e 1;

%e 0, 1;

%e 0, 1, 2;

%e 0, 1, 6, 9;

%e 0, 1, 14, 46, 64;

%e 0, 1, 30, 175, 465, 625;

%e 0, 1, 62, 596, 2471, 5901, 7776;

%e 0, 1, 126, 1925, 11634, 40376, 90433, 117649;

%e 0, 1, 254, 6042, 51570, 243454, 757940, 1626556, 2097152;

%e 0, 1, 510, 18651, 220887, 1376715, 5580021, 16146957, 33609537, 43046721;

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

%K nonn,tabl

%O 0,6

%A _Ran Pan_, Nov 16 2015

%E Edited by _Alois P. Heinz_, Nov 26 2015

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Last modified October 15 18:18 EDT 2018. Contains 316237 sequences. (Running on oeis4.)