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T(n,m) = binomial(m!,n).
3

%I #14 Nov 06 2016 19:16:04

%S 1,2,0,6,1,0,24,15,0,0,120,276,20,0,0,720,7140,2024,15,0,0,5040,

%T 258840,280840,10626,6,0,0,40320,12698280,61949040,8214570,42504,1,0,

%U 0,362880,812831040,21324644880,11104365420,190578024,134596,0,0,0,3628800

%N T(n,m) = binomial(m!,n).

%C T(n,m) = number of n X m arrays with each row a permutation of 1..m and rows lexicographically in strictly increasing order.

%H R. H. Hardin, <a href="/A180397/b180397.txt">Table of n, a(n) for n = 1..1275</a>

%F T(n,m) = binomial(m!,n).

%e Table starts

%e 1 2 6 24 120 720 5040 40320 362880 3628800

%e 0 1 15 276 7140 258840 12698280 812831040 65840765760

%e 0 0 20 2024 280840 61949040 21324644880 10923907290240

%e 0 0 15 10626 8214570 11104365420 26853059065140

%e 0 0 6 42504 190578024 1590145128144

%e 0 0 1 134596 3652745460

%e 0 0 0 346104

%e 0 0 0

%e 0 0

%e 0

%t t[n_, m_] := Binomial[m!, n]; Table[t[m - n + 1, n], {m, 9}, {n, m, 1, -1}] // Flatten (* to display table in Comment *) Table[ t[m, n], {m, 10}, {n, 8}] // TableForm (* _Robert G. Wilson v_, Sep 02 2010 *)

%Y See A105291 for another version.

%Y First row gives A000142.

%Y Main diagonal gives A086687.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Sep 01 2010