A105291 Triangle read by rows: T(m,n) = binomial(m!,n), m>=0, 0 <= n <= m!.

1, 1, 1, 1, 1, 2, 1, 1, 6, 15, 20, 15, 6, 1, 1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1, 1, 120, 7140, 280840, 8214570, 190578024

Offset: 0

Author

N. J. A. Sloane, Sep 03 2010, following a suggestion from R. H. Hardin, Aug 31 2010

Keywords

• nonn
• tabf

Comments

This is the number of nXm arrays with each row a permutation of 1..m, and rows in lexicographically strictly increasing order.

For row 0, remember that 0!=1.

Examples

			Triangle begins:
[1, 1],
[1, 1],
[1, 2, 1],
[1, 6, 15, 20, 15, 6, 1],
[1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1],
...
		

Links

• Alois P. Heinz, Rows n = 0..6, flattened

Crossrefs

See A180397 for another version.

Cf. A007318 (Pascal's triangle), A086687, A109892.

Programs

Mathematica

Flatten[Table[Binomial[m!,n],{m,0,5},{n,0,m!}]] (* Harvey P. Dale, Apr 16 2013 *)