A173279 Irregular triangle read by rows: M(n,k) = (n-2*k)!, k=0..floor(n/2).

1, 1, 2, 1, 6, 1, 24, 2, 1, 120, 6, 1, 720, 24, 2, 1, 5040, 120, 6, 1, 40320, 720, 24, 2, 1, 362880, 5040, 120, 6, 1, 3628800, 40320, 720, 24, 2, 1, 39916800, 362880, 5040, 120, 6, 1, 479001600, 3628800, 40320, 720, 24, 2, 1, 6227020800, 39916800, 362880, 5040, 120, 6, 1, 87178291200

Offset: 0

Author

Gary W. Adamson, Feb 14 2010

Keywords

• nonn
• tabf

Comments

In the limit as j-> infinity, the power M^j approaches the limit described in A173280.

Row sums: sum_{k=0..n/2} M(n,k) = A136580(n).

Examples

			Triangle starts in row n=0 as:
1;
1;
2, 1;
6, 1;
24, 2, 1;
120, 6, 1;
720, 24, 2, 1;
5040, 120, 6, 1;
40320, 720, 24, 2, 1;
362880, 5040, 120, 6, 1;
3628800, 40320, 720, 24, 2, 1;
39916800, 362880, 5040, 120, 6, 1;
479001600, 3628800, 40320, 720, 24, 2, 1;
...
		

Crossrefs

Cf. A000142, A136580, A173280

Programs

Maple

A173279 := proc(n,k) factorial(n-2*k) ; end proc: seq(seq(A173279(n,k),k=0..floor(n/2)),n=0..20) ; # R. J. Mathar, Feb 22 2010

Extensions

keyword tabl replaced by tabf, R. J. Mathar, Feb 22 2010