A229160 Triangle T(n,k) read by rows: T(n,k) = number of permutations on 123...n with exactly one cab pattern and no aj pattern with j<=k, for n>=0, 0<=k<=n.

0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 5, 5, 2, 0, 0, 21, 21, 11, 3, 0, 0, 84, 84, 49, 19, 4, 0, 0, 330, 330, 204, 92, 29, 5, 0, 0, 1287, 1287, 825, 405, 153, 41, 6, 0, 0, 5005, 5005, 3289, 1705, 715, 235, 55, 7, 0, 0, 19448, 19448, 13013, 7007, 3146, 1166, 341, 71, 8, 0, 0

Offset: 0

Author

N. J. A. Sloane, Sep 15 2013

Keywords

• nonn
• tabl

Comments

See Noonan-Zeilberger for precise definition.

Examples

			Triangle begins:
0,
0,0,
0,0,0,
1,1,0,0,
5,5,2,0,0,
21,21,11,3,0,0,
84,84,49,19,4,0,0,
330,330,204,92,29,5,0,0,
1287,1287,825,405,153,41,6,0,0,
5005,5005,3289,1705,715,235,55,7,0,0,
19448,19448,13013,7007,3146,1166,341,71,8,0,0,
...
		

Links

• J. Noonan and D. Zeilberger, [math/9808080] The Enumeration of Permutations With a Prescribed Number of ``Forbidden'' Patterns. Also Adv. in Appl. Math. 17 (1996), no. 4, 381--407. MR1422065 (97j:05003).

Crossrefs

Cf. A228708, A229158, A002054.