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URL: https://oeis.org/A180397

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A180397
T(n,m) = binomial(m!,n).
3
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
1,2
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.
LINKS
FORMULA
T(n,m) = binomial(m!,n).
EXAMPLE
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
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 *)
CROSSREFS
See A105291 for another version.
First row gives A000142.
Main diagonal gives A086687.
Sequence in context: A183189 A330609 A180047 * A347133 A317842 A021489
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 01 2010
STATUS
approved