The 10 tableaux with n=4 cells sorted by largest value in the last row:
:[1 3 4]:[1 4] [1 2 4]:[1] [1 2] [1 3] [1 2 3] [1 2] [1 3] [1 2 3 4]:
:[2] :[2] [3] :[2] [3] [2] [4] [3 4] [2 4] :
: :[3] :[3] [4] [4] :
: : :[4] :
: --2-- : -----3----- : ---------------------4--------------------- :
The 10 ballot sequences of length 4 sorted by the position of the last occurrence of the maximal value:
[1, 2, 1, 1] -> 2 } -- 1
[1, 2, 3, 1] -> 3 \ __ 2
[1, 1, 2, 1] -> 3 /
[1, 2, 3, 4] -> 4 \
[1, 1, 2, 3] -> 4 \
[1, 2, 1, 3] -> 4 \
[1, 1, 1, 2] -> 4 } 7
[1, 1, 2, 2] -> 4 /
[1, 2, 1, 2] -> 4 /
[1, 1, 1, 1] -> 4 /
thus row 4 = [0, 0, 1, 2, 7].
Triangle T(n,k) begins:
00: 1;
01: 0, 1;
02: 0, 0, 2;
03: 0, 0, 1, 3;
04: 0, 0, 1, 2, 7;
05: 0, 0, 1, 3, 8, 14;
06: 0, 0, 1, 4, 11, 19, 41;
07: 0, 0, 1, 7, 19, 34, 64, 107;
08: 0, 0, 1, 11, 32, 62, 119, 202, 337;
09: 0, 0, 1, 21, 64, 131, 248, 418, 671, 1066;
10: 0, 0, 1, 36, 124, 277, 545, 943, 1518, 2361, 3691;
