A263754 - OEIS

%I #15 Feb 13 2024 09:18:02

%S 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,

%T 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,

%U 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

%N 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.

%C Row sums give A000142.

%H Alois P. Heinz, <a href="/A263754/b263754.txt">Rows n = 0..7, flattened</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000110">The number of permutations less than or equal to given permutation in left weak order</a>.

%F Sum_{k=1..n!} k * T(n,k) = A007767(n). - _Alois P. Heinz_, Jun 06 2016

%e Triangle begins:

%e   1;

%e   1;

%e   1,1;

%e   1,2,2,0,0,1;

%e   1,3,4,3,2,3,0,4,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,1;

%e   ...

%Y Cf. A000142, A007767.

%K nonn,tabf

%O 0,6

%A _Christian Stump_, Oct 19 2015

%E Row n=0 prepended by _Alois P. Heinz_, Jun 06 2016