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A229158 Triangle T(n,k) read by rows: T(n,k) = number of permutations on 123...n with exactly two abc patterns and no aj pattern with j<=k, for n>=0, 0<=k<=n.

%I A229158 #13 Sep 17 2013 16:22:28
%S A229158 0,0,0,0,0,0,0,0,0,0,3,3,1,0,0,24,24,12,2,0,0,133,133,74,23,3,0,0,635,
%T A229158 635,371,141,36,4,0,0,2807,2807,1688,709,227,51,5,0,0,11864,11864,
%U A229158 7276,3248,1168,334,68,6,0,0,48756,48756,30340,14121,5459,1771,464,87,7,0,0
%N A229158 Triangle T(n,k) read by rows: T(n,k) = number of permutations on 123...n with exactly two abc patterns and no aj pattern with j<=k, for n>=0, 0<=k<=n.
%C A229158 See Noonan-Zeilberger for precise definition.
%H A229158 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 A229158 Triangle begins:
%e A229158 0,
%e A229158 0,0,
%e A229158 0,0,0,
%e A229158 0,0,0,0,
%e A229158 3,3,1,0,0,
%e A229158 24,24,12,2,0,0,
%e A229158 133,133,74,23,3,0,0,
%e A229158 635,635,371,141,36,4,0,0,
%e A229158 2807,2807,1688,709,227,51,5,0,0,
%e A229158 11864,11864,7276,3248,1168,334,68,6,0,0,
%e A229158 48756,48756,30340,14121,5459,1771,464,87,7,0,0
%e A229158 ...
%Y A229158 Cf. A228708, A001089.
%K A229158 nonn,tabl
%O A229158 0,11
%A A229158 _N. J. A. Sloane_, Sep 15 2013