A218581 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.

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, 496, 0, 1, 34, 149, 392, 826, 1496, 2437, 0, 1, 66, 375, 1120, 2592, 5036, 8615, 13435, 0, 1, 130, 989, 3392, 8698, 18332, 33391, 54548, 82127

Offset: 1

Author

Joerg Arndt, Nov 03 2012

Keywords

• nonn
• tabl

Comments

Row sums are A022493.

Examples

			Triangle starts:
[ 1]  1,
[ 2]  0, 2,
[ 3]  0, 1, 4,
[ 4]  0, 1, 4, 10,
[ 5]  0, 1, 6, 15, 31,
[ 6]  0, 1, 10, 29, 62, 115,
[ 7]  0, 1, 18, 63, 148, 288, 496,
[ 8]  0, 1, 34, 149, 392, 826, 1496, 2437,
[ 9]  0, 1, 66, 375, 1120, 2592, 5036, 8615, 13435,
[10]  0, 1, 130, 989, 3392, 8698, 18332, 33391, 54548, 82127,
[11]  0, 1, 258, 2703, 10768, 30768, 70868, 138635, 239688, 377001, 551384,
...
		

Crossrefs

Cf. A022493 (number of ascent sequences).

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).

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