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

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

Offset: 1

Author

Tilman Piesk, Jul 07 2012

Keywords

• nonn
• tabl
• easy

Comments

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

Examples

			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, ...
		

Links

• Tilman Piesk, Table of n, a(n) for n = 1..2016
• Tilman Piesk, Circular shifts to the left (Arrays of permutations)

Crossrefs

Cf. A051683 (circular shifts to the right), A007489 (column n=1), A000142 (row m=1).

Programs

Mathematica

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 *)