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A298597
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Number T(n,k) of times the value k appears on the parking functions of length n and such that if we replace that value k with k+1 we don't get a parking function.
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3
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1, 2, 2, 9, 6, 9, 64, 36, 36, 64, 625, 320, 270, 320, 625, 7776, 3750, 2880, 2880, 3750, 7776, 117649, 54432, 39375, 35840, 39375, 54432, 117649, 2097152, 941192, 653184, 560000, 560000, 653184, 941192, 2097152, 43046721, 18874368, 12706092, 10450944, 9843750, 10450944, 12706092, 18874368, 43046721
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n,k) = n*binomial(n-1, k-1)*k^(k-2)*(n+1-k)^(n-1-k).
T(n,k) = T(n,n-k).
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EXAMPLE
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Triangle begins:
1;
2, 2;
9, 6, 9;
64, 36, 36, 64;
625, 320, 270, 320, 625;
7776, 3750, 2880, 2880, 3750, 7776;
117649, 54432, 39375, 35840, 39375, 54432, 117649;
2097152, 941192, 653184, 560000, 560000, 653184, 941192, 2097152;
...
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MATHEMATICA
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Table[n Binomial[n - 1, k - 1] k^(k - 2)*(n + 1 - k)^(n - 1 - k), {n, 9}, {k, n}] // Flatten (* Michael De Vlieger, Jan 22 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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