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A199656
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Triangular array read by rows, T(n,k) is the number of functions from {1,2,...,n} into {1,2,...,n} with maximum value of k.
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7
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1, 1, 3, 1, 7, 19, 1, 15, 65, 175, 1, 31, 211, 781, 2101, 1, 63, 665, 3367, 11529, 31031, 1, 127, 2059, 14197, 61741, 201811, 543607, 1, 255, 6305, 58975, 325089, 1288991, 4085185, 11012415
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OFFSET
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1,3
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COMMENTS
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Row sums = A000312.
Main diagonal = A045531.
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LINKS
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Vincenzo Librandi, Rows n = 1..60, flattened
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FORMULA
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T(n,k) = k^n-(k-1)^n.
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EXAMPLE
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Triangle begins:
1
1 3
1 7 19
1 15 65 175
1 31 211 781 2101
1 63 665 3367 11529 31031
1 127 2059 14197 61741 201811 543607 etc.
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MATHEMATICA
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Table[Table[(1-((i-1)/i)^n) i^n, {i, 1, n}], {n, 1, 8}]//Grid
Flatten[Table[k^n - (k-1)^n, {n, 0, 10}, {k, 1, n}]] (* Vincenzo Librandi, Jan 28 2013 *)
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PROG
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(Magma) /* As triangle: */ [[k^n - (k-1)^n: k in [1..n]]: n in [1..9]]; // Vincenzo Librandi, Jan 28 2013
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CROSSREFS
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Cf. A022522, A022523.
Sequence in context: A282605 A281525 A096643 * A221345 A036575 A347485
Adjacent sequences: A199653 A199654 A199655 * A199657 A199658 A199659
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Geoffrey Critzer, Nov 08 2011
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STATUS
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approved
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