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 A137398 Let S be a strictly monotonic sequence of length 2n and let p and q be subsequences of S each of length n such that the least element belongs to p and every element of S belongs to either p or q. The number of ways to select p such that for any index i the exchange of p(i) and q(i) makes at least one of p and q non-monotonic, is given by a(n). 2
 0, 1, 2, 7, 22, 74, 252, 875, 3078, 10950, 39316, 142278, 518364, 1899668, 6997688, 25894579, 96211398, 358779118, 1342323364, 5037146738, 18953759988, 71497359884, 270321915848, 1024217489278, 3888253473180, 14787937448380, 56337410614088, 214967841333868, 821473056041464, 3143521372849960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sequence occurs as the diagonal of the triangle below.   0;   0,   1;   0,   1,   2;   0,   1,   3,   7;   0,   1,   4,  11,  22;   0,   1,   5,  16,  38,  74;   0,   1,   6,  22,  60, 134, 252;   0,   1,   7,  29,  89, 223, 475, 875; The triangle is generated by: b(n,0)=0; b(n,1)=1; b(n,k)=2b(k-2,k-2)+ Sum_{i=k-1..n} b(i,k-1) for 2<=k<=n; or alternatively, for 2<=k

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)