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A089479
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Triangle T(n,k) read by rows, where T(n,k) = number of times the permanent of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= n!.
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9
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0, 1, 1, 1, 9, 6, 1, 265, 150, 69, 18, 9, 0, 1, 27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288, 96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1, 10363361, 3513720, 4339440, 2626800, 3015450, 1451400, 1872800, 962400, 1295700, 425400, 873000
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OFFSET
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0,5
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COMMENTS
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The last element of each row is 1, corresponding to the n X n "all 1" matrix with permanent = n!. The first 4 rows were provided by Wouter Meeussen. The 6th row was computed by Gordon F. Royle: 13906734081, 2722682160, 4513642920, 3177532800, 4466769300, 2396826720, 3710999520, 2065521600, 3253760550, 1468314000, 2641593600, 1350475200, 2210277600, 1034061120,... .
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LINKS
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FORMULA
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For n>2, T(n,n!-(n-1)!) = n^2, the number of matrices with exactly one 0 entry. (End)
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EXAMPLE
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Triangle begins:
0, 1;
1, 1;
9, 6, 1;
265, 150, 69, 18, 9, 0, 1;
27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288,
96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1;
...
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CROSSREFS
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T(n,0) = A088672(n), T(n,1) = A089482(n). The n-th row of the table contains A087983(n) nonzero entries. For n>2 A089477(n) gives the position of the first zero entry in the n-th row.
Cf. A089480 (occurrence counts for permanents of non-singular (0,1)-matrices), A089481 (occurrence counts for permanents of singular (0,1)-matrices).
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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