A263754 - OEIS

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

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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

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