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A208651
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Number of paths through the subset array whose trace is a permutation of (1,2,...,n); see Comments.
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2
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1, 2, 12, 216, 11520, 1800000, 816480000, 1067311728000, 3996990937497600, 42672954793151692800, 1293547461212160000000000, 110950032218933108678400000000, 26847804299643702075375747072000000
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OFFSET
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1,2
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COMMENTS
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See A208650. The trace of a path is a permutation of (1,2,...,n) if and only if the range of the path is {1,2,...,n}.
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LINKS
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EXAMPLE
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Taking n=3:
row 1: {1},{2},{3} ---------> 1,2,3
row 2: {1,2},{1,3},{2,3} ---> 1,1,2,2,3,3
row 3: {1,2,3} -------------> 1,2,3
3 ways to choose a number from row 1,
4 ways to choose a different number from row 2,
1 way to choose remaining number from row 3.
Total: a(3) = 1*4*3 = 12 paths.
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MATHEMATICA
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p[n_]:=Product[Binomial[n-1, k], {k, 1, n-1}]
Table[p[n], {n, 1, 20}] (* A001142(n-1) *)
Table[p[n]*n, {n, 1, 20}] (* A208650 *)
Table[p[n]*n!, {n, 1, 20}] (* A208651 *)
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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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