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A263412 Triangle read by rows: T(n>=0, 0<=k<=A161680(n)) is the number of standard tableaux of size n whose shape contains k attacking pairs.

%I A263412 #11 Nov 15 2015 18:53:44
%S A263412 1,1,1,1,1,2,0,1,1,3,0,5,0,0,1,1,4,0,11,0,5,4,0,0,0,1,1,5,0,19,0,21,
%T A263412 10,0,9,5,5,0,0,0,0,1,1,6,0,29,0,49,20,21,35,21,15,0,28,0,0,6,0,0,0,0,
%U A263412 0,1,1,7,0,41,0,92,35,84,90,56,91,42,134,0,0,21,28,20,14,0,0,7,0,0,0,0,0,0,1
%N A263412 Triangle read by rows: T(n>=0, 0<=k<=A161680(n)) is the number of standard tableaux of size n whose shape contains k attacking pairs.
%C A263412 Row sums give A000085.
%H A263412 Alois P. Heinz, <a href="/A263412/b263412.txt">Rows n = 0..50, flattened</a>
%H A263412 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000016">The number of attacking pairs of a standard tableau</a>.
%e A263412 Triangle begins:
%e A263412 1;
%e A263412 1;
%e A263412 1,1;
%e A263412 1,2,0,1;
%e A263412 1,3,0,5,0,0,1;
%e A263412 1,4,0,11,0,5,4,0,0,0,1;
%e A263412 1,5,0,19,0,21,10,0,9,5,5,0,0,0,0,1;
%e A263412 1,6,0,29,0,49,20,21,35,21,15,0,28,0,0,6,0,0,0,0,0,1;
%e A263412 1,7,0,41,0,92,35,84,90,56,91,42,134,0,0,21,28,20,14,0,0,7,0,0,0,0,0,0,1;
%e A263412 ...
%Y A263412 Cf. A000085, A161680.
%K A263412 nonn,tabf
%O A263412 0,6
%A A263412 _Christian Stump_, Oct 17 2015
%E A263412 Two terms (for rows 0 and 1) prepended by _Alois P. Heinz_, Nov 15 2015