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A211370 Array read by antidiagonals: T(m,n) = Sum( n <= i <= m+n-1 ) i!.

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