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A366503 Triangle read by rows: T(n,k) = number of permutations of (1, 2, ..., n) with longest monotonic subsequence of length k (1<=k<=n).

%I A366503 #36 Nov 05 2023 14:36:36
%S A366503 1,0,2,0,4,2,0,4,18,2,0,0,86,32,2,0,0,306,362,50,2,0,0,882,3242,842,
%T A366503 72,2,0,0,1764,24564,12210,1682,98,2,0,0,1764,163872,161158,32930,
%U A366503 3026,128,2,0,0,0,985032,1969348,592652,76562,5042,162,2
%N A366503 Triangle read by rows: T(n,k) = number of permutations of (1, 2, ..., n) with longest monotonic subsequence of length k (1<=k<=n).
%H A366503 Douglas Boffey, <a href="/A366503/a366503.cc.txt">C++ program used to generate the sequence</a>
%e A366503 Triangle begins:
%e A366503   1;
%e A366503   0, 2;
%e A366503   0, 4,    2;
%e A366503   0, 4,   18,     2;
%e A366503   0, 0,   86,    32,     2;
%e A366503   0, 0,  306,   362,    50,    2;
%e A366503   0, 0,  882,  3242,   842,   72,  2;
%e A366503   0, 0, 1764, 24564, 12210, 1682, 98, 2;
%e A366503   ...
%e A366503 The T(4, 2) = 4 permutations are: 2,1,4,3; 2,4,1,3; 3,1,4,2; 3,4,1,2.
%Y A366503 Row sums are A000142.
%Y A366503 Cf. A047874.
%K A366503 nonn,tabl
%O A366503 1,3
%A A366503 _Douglas Boffey_, Oct 12 2023