A181511 Triangle T(n,k) = n!/(n-k)! read by rows, 0 <= k < n.

1, 1, 2, 1, 3, 6, 1, 4, 12, 24, 1, 5, 20, 60, 120, 1, 6, 30, 120, 360, 720, 1, 7, 42, 210, 840, 2520, 5040, 1, 8, 56, 336, 1680, 6720, 20160, 40320, 1, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 1, 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800

Offset: 1

Author

Alford Arnold, Oct 26 2010

Keywords

• nonn
• tabl
• easy

Comments

Row n contains the same set of values as row A181512(n,.), which are related to labeled rooted trees (A000169) and Bell numbers (A000110) respectively.

Examples

			The triangle begins:
  1;
  1,  2;
  1,  3,  6;
  1,  4, 12, 24;
which is A181512 without duplicates.
		

Links

• Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A002627 (row sums).

Programs

Haskell

a181511 n k = a181511_tabl !! (n-1) !! k
a181511_row n = a181511_tabl !! (n-1)
a181511_tabl = tail $ map init a008279_tabl
-- Reinhard Zumkeller, Nov 18 2012

Maple

A181511 := proc(n,k) n!/(n-k)! ; end proc:
seq(seq(A181511(n,k),k=0..n-1),n=1..16) ; # R. J. Mathar, Mar 03 2011

Formula

T(n,k) = A008279(n,k). - R. J. Mathar, Mar 03 2011