A366503 - OEIS

%I #36 Nov 05 2023 14:36:36

%S 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 72,2,0,0,1764,24564,12210,1682,98,2,0,0,1764,163872,161158,32930,

%U 3026,128,2,0,0,0,985032,1969348,592652,76562,5042,162,2

%N 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 Douglas Boffey, <a href="/A366503/a366503.cc.txt">C++ program used to generate the sequence</a>

%e Triangle begins:

%e   1;

%e   0, 2;

%e   0, 4,    2;

%e   0, 4,   18,     2;

%e   0, 0,   86,    32,     2;

%e   0, 0,  306,   362,    50,    2;

%e   0, 0,  882,  3242,   842,   72,  2;

%e   0, 0, 1764, 24564, 12210, 1682, 98, 2;

%e   ...

%e The T(4, 2) = 4 permutations are: 2,1,4,3; 2,4,1,3; 3,1,4,2; 3,4,1,2.

%Y Row sums are A000142.

%Y Cf. A047874.

%K nonn,tabl

%O 1,3

%A _Douglas Boffey_, Oct 12 2023