A180397 T(n,m) = binomial(m!,n).

1, 2, 0, 6, 1, 0, 24, 15, 0, 0, 120, 276, 20, 0, 0, 720, 7140, 2024, 15, 0, 0, 5040, 258840, 280840, 10626, 6, 0, 0, 40320, 12698280, 61949040, 8214570, 42504, 1, 0, 0, 362880, 812831040, 21324644880, 11104365420, 190578024, 134596, 0, 0, 0, 3628800

Offset: 1

Author

R. H. Hardin, Sep 01 2010

Keywords

• nonn
• tabl

Comments

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

Examples

			Table starts
1 2 6 24 120 720 5040 40320 362880 3628800
0 1 15 276 7140 258840 12698280 812831040 65840765760
0 0 20 2024 280840 61949040 21324644880 10923907290240
0 0 15 10626 8214570 11104365420 26853059065140
0 0 6 42504 190578024 1590145128144
0 0 1 134596 3652745460
0 0 0 346104
0 0 0
0 0
0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1275

Crossrefs

See A105291 for another version.

First row gives A000142.

Main diagonal gives A086687.

Programs

Mathematica

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 *)

Formula

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