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A103690
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Triangle read by rows: T(n,k)=binomial(n,k-1)*k^(k-1)*(n+1-k)^(n-k) (1<=k<=n).
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0
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1, 2, 4, 9, 12, 27, 64, 72, 108, 256, 625, 640, 810, 1280, 3125, 7776, 7500, 8640, 11520, 18750, 46656, 117649, 108864, 118125, 143360, 196875, 326592, 823543, 2097152, 1882384, 1959552, 2240000, 2800000, 3919104, 6588344, 16777216, 43046721
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OFFSET
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1,2
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(p.27, Problem 1.2.6 (b)).
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LINKS
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FORMULA
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T(n, k)=binomial(n, k-1)*k^(k-1)*(n+1-k)^(n-k) (1<=k<=n).
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MAPLE
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T:=proc(n, k) if k<=n then binomial(n, k-1)*k^(k-1)*(n+1-k)^(n-k) else 0 fi end: for n from 1 to 9 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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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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