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Triangle read by rows: T(n,k) is the number of ascent sequences of length n with last occurrence of the maximal value at position k-1.
5

%I #8 Nov 09 2012 17:56:39

%S 1,0,2,0,1,4,0,1,4,10,0,1,6,15,31,0,1,10,29,62,115,0,1,18,63,148,288,

%T 496,0,1,34,149,392,826,1496,2437,0,1,66,375,1120,2592,5036,8615,

%U 13435,0,1,130,989,3392,8698,18332,33391,54548,82127

%N Triangle read by rows: T(n,k) is the number of ascent sequences of length n with last occurrence of the maximal value at position k-1.

%C Row sums are A022493.

%e Triangle starts:

%e [ 1] 1,

%e [ 2] 0, 2,

%e [ 3] 0, 1, 4,

%e [ 4] 0, 1, 4, 10,

%e [ 5] 0, 1, 6, 15, 31,

%e [ 6] 0, 1, 10, 29, 62, 115,

%e [ 7] 0, 1, 18, 63, 148, 288, 496,

%e [ 8] 0, 1, 34, 149, 392, 826, 1496, 2437,

%e [ 9] 0, 1, 66, 375, 1120, 2592, 5036, 8615, 13435,

%e [10] 0, 1, 130, 989, 3392, 8698, 18332, 33391, 54548, 82127,

%e [11] 0, 1, 258, 2703, 10768, 30768, 70868, 138635, 239688, 377001, 551384,

%e ...

%Y Cf. A022493 (number of ascent sequences).

%Y Cf. A218579 (ascent sequences with last zero at position k-1), A218580 (ascent sequences with first occurrence of the maximal value at position k-1).

%Y Cf. A137251 (ascent sequences with k ascents), A218577 (ascent sequences with maximal element k), A175579 (ascent sequences with k zeros).

%K nonn,tabl

%O 1,3

%A _Joerg Arndt_, Nov 03 2012