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A085838 Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,1,1,2,1,3,1,4,1,5,1,6,...], where DELTA is Deléham's operator defined in A084938.

%I A085838 #20 Feb 19 2020 12:06:08
%S A085838 1,0,1,0,1,2,0,1,5,5,0,1,9,22,15,0,1,14,60,98,52,0,1,20,130,366,457,
%T A085838 203,0,1,27,245,1031,2190,2254,877,0,1,35,420,2436,7652,13251,11788,
%U A085838 4140,0,1,44,672,5096,21862,55499,82288,65330,21147,0,1,54,1020,9744,54216,186595,402582,528400,382948,115975
%N A085838 Triangle T(n,k) read by rows; given by [0,1,0,1,0,1,0,1,...] DELTA [1,1,1,2,1,3,1,4,1,5,1,6,...], where DELTA is Deléham's operator defined in A084938.
%C A085838 T(n,k) appears to be the number of indecomposable permutations of [n+1] that avoid both of the dashed patterns 41-32 and 32-41 and contain n+1-k right-to-left minima. For example, T(3,1)=1 counts 4123 with 3 right-to-left minima; T(3,2)=5 counts 2413, 3142, 3412, 4213, 4312, each with 2 right-to-left minima; and T(3,3)=5 counts 2341, 2431, 3421, 4231, 4321, each with 1 right-to-left minimum. - _David Callan_, Aug 27 2014
%H A085838 Alois P. Heinz, <a href="/A085838/b085838.txt">Rows n = 0..140, flattened</a>
%F A085838 Sum_{k=0..n} (-x)^(n-k)*T(n,k) = A090365(n), A000110(n), A000012(n), A010892(n) for x=-1, 0, 1, 2. - _Philippe Deléham_, Oct 26 2006
%e A085838 1;
%e A085838 0, 1;
%e A085838 0, 1,  2;
%e A085838 0, 1,  5,  5;
%e A085838 0, 1,  9,  22,   15;
%e A085838 0, 1, 14,  60,   98,   52;
%e A085838 0, 1, 20, 130,  366,  457,   203;
%e A085838 0, 1, 27, 245, 1031, 2190,  2254,   877;
%e A085838 0, 1, 35, 420, 2436, 7652, 13251, 11788, 4140;
%t A085838 m = 13;
%t A085838 (* DELTA is defined in A084938 *)
%t A085838 DELTA[Table[{0, 1}, {m/2 // Ceiling}] // Flatten, LinearRecurrence[{0, 2, 0, -1}, {1, 1, 1, 2}, m], m] // Flatten (* _Jean-François Alcover_, Feb 19 2020 *)
%Y A085838 Cf. A084938, A085791.
%Y A085838 Diagonals : A000007, A000012, A000096, A000110. Row sums : A090365
%K A085838 nonn,tabl
%O A085838 0,6
%A A085838 _N. J. A. Sloane_, Aug 16 2003