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

0,6

Comments

Row sums give A000142.

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.

Formula

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

Example

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;
  ...

Crossrefs

Cf. A000142, A007767.

Sequence in context: A318753 A318757 A263834 * A328800 A328802 A355245

Adjacent sequences: A263751 A263752 A263753 * A263755 A263756 A263757

Keyword

nonn,tabf

Author

Christian Stump, Oct 19 2015

Extensions

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

Status

approved