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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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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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KEYWORD
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AUTHOR
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STATUS
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approved
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