A136572 Triangle read by rows: row n consists of n zeros followed by n!.

1, 0, 1, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, 5040, 0, 0, 0, 0, 0, 0, 0, 0, 40320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 362880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3628800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39916800

Offset: 0

Author

Gary W. Adamson, Jan 07 2008

Keywords

• nonn
• tabl

Comments

A136572 * A007318 = A021012(unsigned). A007318 * A136572 = A008279.

Examples

			First few rows of the triangle:
  1;
  0, 1;
  0, 0, 2;
  0, 0, 0, 6;
  0, 0, 0, 0, 24;
  0, 0, 0, 0,  0, 120;
  ...
		

Links

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

Crossrefs

Cf. A000142, A021012, A008279.

Programs

Haskell

a136572 n k = a136572_tabl !! n !! k
a136572_row n = a136572_tabl !! n
a136572_tabl = map fst $ iterate f ([1], 1) where
   f (row, i) = (0 : map (* i) row, i + 1)
-- Reinhard Zumkeller, Nov 18 2012

Mathematica

Table[PadLeft[{n!},n+1,0],{n,0,20}]//Flatten (* Harvey P. Dale, Oct 22 2016 *)

Formula

Triangle, n zeros followed by n! T(n,k): n! * 0^(n-k), 0 <= k <= n.

As an infinite lower triangular matrix, A000142 (1, 1, 2, 6, 24, 120, ...) in the main diagonal and the rest zeros.