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%I #20 Apr 30 2017 22:38:58
%S 1,2,3,6,8,9,24,30,32,33,120,144,150,152,153,720,840,864,870,872,873,
%T 5040,5760,5880,5904,5910,5912,5913,40320,45360,46080,46200,46224,
%U 46230,46232,46233,362880,403200,408240,408960,409080,409104,409110,409112,409113
%N Array read by antidiagonals: T(m,n) = Sum( n <= i <= m+n-1 ) i!.
%C 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
%H Tilman Piesk, <a href="/A211370/b211370.txt">Table of n, a(n) for n = 1..2016</a>
%H Tilman Piesk, <a href="https://commons.wikimedia.org/wiki/File:Array_of_permutations;_circular_shift,_left.svg">Circular shifts to the left</a> (<a href="https://en.wikiversity.org/wiki/Arrays_of_permutations#arrays4">Arrays of permutations</a>)
%e T(3,2) = Sum( 2 <= i <= 4 ) i! = 2! + 3! + 4! = 32.
%e The array starts:
%e 1, 2, 6, 24, 120, 720, ...
%e 3, 8, 30, 144, 840, 5760, ...
%e 9, 32, 150, 864, 5880, 46080, ...
%e 33, 152, 870, 5904, 46200, 408960, ...
%e 153, 872, 5910, 46224, 409080, 4037760, ...
%e 873, 5912, 46230, 409104, 4037880, 43954560, ...
%t 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 *)
%Y Cf. A051683 (circular shifts to the right), A007489 (column n=1), A000142 (row m=1).
%K nonn,tabl,easy
%O 1,2
%A _Tilman Piesk_, Jul 07 2012
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