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%I #9 Oct 25 2015 15:40:38
%S 1,1,1,1,1,1,1,1,1,2,3,4,4,4,3,2,1,1
%N Triangle read by rows: T(n>=1, k>=0) is the number of standard tableaux of size n and (Haglund and Stevens) inversion number k.
%C Row sums give A000085, n >= 2.
%C The inversion number is the total number of inversion pairs for the tableau. An inversion pair is defined as a pair of cells (a,b), (x,y) such that the content of (x,y) is greater than the content of (a,b) and (x,y) is north of the inversion path of (a,b).
%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000059">The inversion number of a standard tableau as defined by Haglund and Stevens</a>.
%H J. Haglund and L. Stevens, <a href="http://www.emis.de/journals/SLC/wpapers/s56hagstev.pdf">An extension of the Foata map to standard Young tableaux</a>, Séminaire Lotharingien de Combinatoire 56 (2006), Article B56c.
%e Triangle begins:
%e 1,1,
%e 1,1,1,1,
%e 1,1,2,3,4,4,4,3,2,1,1,
%e ...
%Y Cf. A000085.
%K nonn,tabf,more
%O 1,10
%A _Christian Stump_, Oct 17 2015
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