%I #8 Nov 06 2016 13:04:54

%S 1,1,1,1,1,2,1,1,6,15,20,15,6,1,1,24,276,2024,10626,42504,134596,

%T 346104,735471,1307504,1961256,2496144,2704156,2496144,1961256,

%U 1307504,735471,346104,134596,42504,10626,2024,276,24,1,1,120,7140,280840,8214570,190578024

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

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

%C For row 0, remember that 0!=1.

%H Alois P. Heinz, <a href="/A105291/b105291.txt">Rows n = 0..6, flattened</a>

%e Triangle begins:

%e [1, 1],

%e [1, 1],

%e [1, 2, 1],

%e [1, 6, 15, 20, 15, 6, 1],

%e [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],

%e ...

%t Flatten[Table[Binomial[m!,n],{m,0,5},{n,0,m!}]] (* _Harvey P. Dale_, Apr 16 2013 *)

%Y See A180397 for another version.

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

%K nonn,tabf

%O 0,6

%A _N. J. A. Sloane_, Sep 03 2010, following a suggestion from _R. H. Hardin_, Aug 31 2010