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

0,6

Comments

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

Links

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

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.

Example

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;
  ...

Mathematica

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

Prog

(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

Crossrefs

Cf. A000142, A021012, A008279.

Sequence in context: A051883 A376202 A132792 * A339016 A262679 A326390

Adjacent sequences: A136569 A136570 A136571 * A136573 A136574 A136575

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 07 2008

Status

approved