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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.

%I A263754 #15 Feb 13 2024 09:18:02
%S A263754 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 A263754 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 A263754 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 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.
%C A263754 Row sums give A000142.
%H A263754 Alois P. Heinz, <a href="/A263754/b263754.txt">Rows n = 0..7, flattened</a>
%H A263754 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 A263754 Sum_{k=1..n!} k * T(n,k) = A007767(n). - _Alois P. Heinz_, Jun 06 2016
%e A263754 Triangle begins:
%e A263754   1;
%e A263754   1;
%e A263754   1,1;
%e A263754   1,2,2,0,0,1;
%e A263754   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 A263754   ...
%Y A263754 Cf. A000142, A007767.
%K A263754 nonn,tabf
%O A263754 0,6
%A A263754 _Christian Stump_, Oct 19 2015
%E A263754 Row n=0 prepended by _Alois P. Heinz_, Jun 06 2016