A258683 Total number of permutations on {1,2,...,n} that have a unique longest increasing subsequence and a unique longest decreasing subsequence.

1, 0, 0, 0, 2, 16, 120, 938, 8014, 74060, 748628, 8163156, 96429784

Offset: 1

Author

Manfred Scheucher, Jun 07 2015

Keywords

• nonn
• more

Comments

By definition, a(n) <= A167995(n).

Examples

			the two permutation of {1,2,...,5}:
{2, 5, 3, 1, 4}
{4, 1, 3, 5, 2}
8 of the 16 permutations of {1,2,...,6} (others reversed):
{1, 3, 6, 4, 2, 5}
{1, 5, 2, 4, 6, 3}
{2, 3, 6, 4, 1, 5}
{2, 5, 3, 1, 4, 6}
{2, 6, 3, 1, 4, 5}
{2, 6, 5, 3, 1, 4}
{3, 6, 4, 2, 1, 5}
{3, 6, 4, 2, 5, 1}
		

Links

• Manfred Scheucher, C Code

Crossrefs

Cf. A167995, A167999, A168502.

Programs

Sage

def A258683(n):
    return len([p for p in permutations(n) if len(p.longest_increasing_subsequences())* len(p.reverse().longest_increasing_subsequences())==1])
# Manfred Scheucher, Jun 07 2015