A263754 Triangle read by rows: T(n,k) (n>=0, 1<=k<=n!) is the number of permutations pi of n such that there are k permutations <= pi in the left weak order.

1, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 3, 4, 3, 2, 3, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 6, 7, 6, 9, 4, 10, 4, 8, 2, 8, 0, 4, 8, 2, 0, 4, 0, 9, 0, 0, 0, 2, 4, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Christian Stump, Oct 19 2015

Keywords

• nonn
• tabf

Comments

Row sums give A000142.

Examples

			Triangle begins:
  1;
  1;
  1,1;
  1,2,2,0,0,1;
  1,3,4,3,2,3,0,4,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,1;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..7, flattened
• FindStat - Combinatorial Statistic Finder, The number of permutations less than or equal to given permutation in left weak order.

Crossrefs

Cf. A000142, A007767.

Formula

Sum_{k=1..n!} k * T(n,k) = A007767(n). - Alois P. Heinz, Jun 06 2016

Extensions

Row n=0 prepended by Alois P. Heinz, Jun 06 2016