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.

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, 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, 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

Offset: 0

Author

Christian Stump, Oct 17 2015

Keywords

• nonn
• tabf

Comments

Row sums give A000085.

Examples

			Triangle begins:
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;
1,5,0,19,0,21,10,0,9,5,5,0,0,0,0,1;
1,6,0,29,0,49,20,21,35,21,15,0,28,0,0,6,0,0,0,0,0,1;
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;
...
		

Links

• Alois P. Heinz, Rows n = 0..50, flattened
• FindStat - Combinatorial Statistic Finder, The number of attacking pairs of a standard tableau.

Crossrefs

Cf. A000085, A161680.

Extensions

Two terms (for rows 0 and 1) prepended by Alois P. Heinz, Nov 15 2015