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

0,6

Comments

Row sums give A000085.

Links

Alois P. Heinz, Rows n = 0..50, flattened

FindStat - Combinatorial Statistic Finder, The number of attacking pairs of a standard tableau.

Example

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;
...

Crossrefs

Cf. A000085, A161680.

Sequence in context: A055186 A217760 A339218 * A321258 A331510 A319854

Adjacent sequences: A263409 A263410 A263411 * A263413 A263414 A263415

Keyword

nonn,tabf

Author

Christian Stump, Oct 17 2015

Extensions

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

Status

approved