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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.

%I A229160 #5 Sep 15 2013 13:26:18
%S A229160 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,
%T A229160 330,204,92,29,5,0,0,1287,1287,825,405,153,41,6,0,0,5005,5005,3289,
%U A229160 1705,715,235,55,7,0,0,19448,19448,13013,7007,3146,1166,341,71,8,0,0
%N 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.
%C A229160 See Noonan-Zeilberger for precise definition.
%H A229160 J. Noonan and D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9808080">[math/9808080] The Enumeration of Permutations With a Prescribed Number of ``Forbidden'' Patterns</a>. Also Adv. in Appl. Math. 17 (1996), no. 4, 381--407. MR1422065 (97j:05003).
%e A229160 Triangle begins:
%e A229160 0,
%e A229160 0,0,
%e A229160 0,0,0,
%e A229160 1,1,0,0,
%e A229160 5,5,2,0,0,
%e A229160 21,21,11,3,0,0,
%e A229160 84,84,49,19,4,0,0,
%e A229160 330,330,204,92,29,5,0,0,
%e A229160 1287,1287,825,405,153,41,6,0,0,
%e A229160 5005,5005,3289,1705,715,235,55,7,0,0,
%e A229160 19448,19448,13013,7007,3146,1166,341,71,8,0,0,
%e A229160 ...
%Y A229160 Cf. A228708, A229158, A002054.
%K A229160 nonn,tabl
%O A229160 0,11
%A A229160 _N. J. A. Sloane_, Sep 15 2013