A122851 Number triangle T(n,k) = C(k,n-k)*(n-k)!.

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 2, 3, 1, 0, 0, 0, 6, 4, 1, 0, 0, 0, 6, 12, 5, 1, 0, 0, 0, 0, 24, 20, 6, 1, 0, 0, 0, 0, 24, 60, 30, 7, 1, 0, 0, 0, 0, 0, 120, 120, 42, 8, 1, 0, 0, 0, 0, 0, 120, 360, 210, 56, 9, 1, 0, 0, 0, 0, 0, 0, 720, 840, 336, 72, 10, 1

Offset: 0

Author

Paul Barry, Sep 14 2006

Keywords

• nonn
• tabl
• easy

Comments

Row sums are A122852.

Triangle T(n,k), read by rows, given by (0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,...) DELTA (1,0,0,-1,2,0,0,-2,3,0,0,-3,4,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 12 2011

Examples

			Triangle begins
  1;
  0, 1;
  0, 1, 1;
  0, 0, 2, 1;
  0, 0, 2, 3,  1;
  0, 0, 0, 6,  4,  1;
  0, 0, 0, 6, 12,  5, 1;
  0, 0, 0, 0, 24, 20, 6, 1;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Crossrefs

Cf. A094587, A242653.

T(2n,n) gives A000142.

Programs

Magma

/* As triangle: */ [[Binomial(k,n-k)*Factorial(n-k): k in [0..n]]: n in [0.. 7]]; // Vincenzo Librandi, Apr 24 2015

Mathematica

Flatten[Table[Binomial[k,n-k](n-k)!,{n,0,10},{k,0,n}]] (* Harvey P. Dale, May 16 2012 *)

Formula

Number triangle T(n,k) = [k<=n]*k!/(2k-n)!.

T(n,k) = A008279(k,n-k). - Danny Rorabaugh, Apr 23 2015