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A211370
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Array read by antidiagonals: T(m,n) = Sum( n <= i <= m+n-1 ) i!.
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3
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1, 2, 3, 6, 8, 9, 24, 30, 32, 33, 120, 144, 150, 152, 153, 720, 840, 864, 870, 872, 873, 5040, 5760, 5880, 5904, 5910, 5912, 5913, 40320, 45360, 46080, 46200, 46224, 46230, 46232, 46233, 362880, 403200, 408240, 408960, 409080, 409104, 409110, 409112, 409113
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OFFSET
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1,2
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COMMENTS
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When the numbers denote finite permutations (as row numbers of A055089) these are the circular shifts to the left within an interval. The subsequence A007489 then denotes the circular shifts that start with the first element. Compare A051683 for circular shifts to the right. - Tilman Piesk, Apr 29 2017
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LINKS
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Tilman Piesk, Table of n, a(n) for n = 1..2016
Tilman Piesk, Circular shifts to the left (Arrays of permutations)
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EXAMPLE
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T(3,2) = Sum( 2 <= i <= 4 ) i! = 2! + 3! + 4! = 32.
The array starts:
1, 2, 6, 24, 120, 720, ...
3, 8, 30, 144, 840, 5760, ...
9, 32, 150, 864, 5880, 46080, ...
33, 152, 870, 5904, 46200, 408960, ...
153, 872, 5910, 46224, 409080, 4037760, ...
873, 5912, 46230, 409104, 4037880, 43954560, ...
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MATHEMATICA
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Table[Function[m, Sum[ i!, {i, n, m + n - 1}]][k - n + 1], {k, 9}, {n, k, 1, -1}] // Flatten (* Michael De Vlieger, Apr 30 2017 *)
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CROSSREFS
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Cf. A051683 (circular shifts to the right), A007489 (column n=1), A000142 (row m=1).
Sequence in context: A289943 A089437 A146768 * A122479 A285306 A047403
Adjacent sequences: A211367 A211368 A211369 * A211371 A211372 A211373
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Tilman Piesk, Jul 07 2012
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STATUS
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approved
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