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A276995
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Triangle read by rows, T(n,k) = k^(n-k)*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.
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1
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1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 2, 4, 0, 1, 0, 9, 16, 9, 0, 1, 0, 44, 144, 54, 16, 0, 1, 0, 265, 1408, 729, 128, 25, 0, 1, 0, 1854, 16960, 10692, 2304, 250, 36, 0, 1, 0, 14833, 237312, 193185, 45056, 5625, 432, 49, 0, 1
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OFFSET
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0,12
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LINKS
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FORMULA
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T(n,k) = k^(n-k)*Gamma(1+n-k,-1)/exp(1).
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EXAMPLE
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Triangle starts:
1;
0, 1;
0, 0, 1;
0, 1, 0, 1;
0, 2, 4, 0, 1;
0, 9, 16, 9, 0, 1;
0, 44, 144, 54, 16, 0, 1;
0, 265, 1408, 729, 128, 25, 0, 1;
0, 1854, 16960, 10692, 2304, 250, 36, 0, 1;
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MAPLE
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T := (n, k) -> A000166(n-k)*k^(n-k): for n from 0 to 9 do seq(T(n, k), k=0..n) od;
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MATHEMATICA
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Table[If[n-k == 0, 1, k^(n-k) Subfactorial[n-k]], {n, 0, 10}, {k, 0, n}] // Flatten
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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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