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

1,2

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

Links

Tilman Piesk, Table of n, a(n) for n = 1..2016

Tilman Piesk, Circular shifts to the left (Arrays of permutations)

Example

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, ...

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 *)

Crossrefs

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

Sequence in context: A089437 A146768 A364958 * A122479 A351125 A334747

Adjacent sequences: A211367 A211368 A211369 * A211371 A211372 A211373

Keyword

nonn,tabl,easy

Author

Tilman Piesk, Jul 07 2012

Status

approved