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).

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, 72, 2, 0, 0, 1764, 24564, 12210, 1682, 98, 2, 0, 0, 1764, 163872, 161158, 32930, 3026, 128, 2, 0, 0, 0, 985032, 1969348, 592652, 76562, 5042, 162, 2

Offset: 1

Author

Douglas Boffey, Oct 12 2023

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  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,   72,  2;
  0, 0, 1764, 24564, 12210, 1682, 98, 2;
  ...
The T(4, 2) = 4 permutations are: 2,1,4,3; 2,4,1,3; 3,1,4,2; 3,4,1,2.
		

Links

• Douglas Boffey, C++ program used to generate the sequence

Crossrefs

Row sums are A000142.

Cf. A047874.