%I #11 Oct 23 2015 13:29:06
%S 2,3,1,5,3,2,7,6,7,5,1,11,12,16,16,12,6,3,15,20,31,38,41,36,26,15,7,3,
%T 22,34,58,79,98,107,107,89,71,50,28,14,6,1
%N Triangle read by rows: T(n>=2, k>=0) is the number of standard tableaux of size n and Shynar inversion number k.
%C Row sums give A000085, n >= 2.
%C Shynar's inversion number is the number of inversion pairs in a standard Young tableau, where an inversion pair is defined as a pair of integers (x,y) such that y > x and y appears strictly southwest of x in the tableau.
%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000057">The Shynar inversion number of a standard tableau</a>.
%H Michael Shynar, <a href="http://www.fpsac.org/FPSAC04/ARTICLES/Shynar.pdf">On Inversions in Standard Young Tableaux</a>, Formal Power Series and Algebraic Combinatorics, 2004.
%e Triangle begins:
%e 2,
%e 3,1,
%e 5,3,2,
%e 7,6,7,5,1,
%e 11,12,16,16,12,6,3,
%e 15,20,31,38,41,36,26,15,7,3,
%e 22,34,58,79,98,107,107,89,71,50,28,14,6,1,
%e ...
%Y Cf. A000085.
%K nonn,tabf,more
%O 2,1
%A _Christian Stump_, Oct 17 2015