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A323295
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Number of ways to fill a matrix with the first n positive integers.
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12
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1, 1, 4, 12, 72, 240, 2880, 10080, 161280, 1088640, 14515200, 79833600, 2874009600, 12454041600, 348713164800, 5230697472000, 104613949440000, 711374856192000, 38414242234368000, 243290200817664000, 14597412049059840000, 204363768686837760000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = A000005(n) * n! for n > 0, a(0) = 1.
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EXAMPLE
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The a(4) = 72 matrices consist of:
24 row/column permutations of [1 2 3 4]
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4 row/column permutations of [1 2]
[3 4]
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4 row/column permutations of [1 2]
[4 3]
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4 row/column permutations of [1 3]
[2 4]
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4 row/column permutations of [1 3]
[4 2]
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4 row/column permutations of [1 4]
[2 3]
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4 row/column permutations of [1 4]
[3 2]
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24 row/column permutations of [1]
[2]
[3]
[4]
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MATHEMATICA
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Join[{1}, Table[DivisorSigma[0, n]*n!, {n, 30}]]
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PROG
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(PARI) a(n) = if (n==0, 1, numdiv(n)*n!); \\ Michel Marcus, Jan 15 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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