A105725 Triangle read by rows: T(n,k)=(n+k)!/k! (0<=k<=n-1; n>=1).

1, 2, 6, 6, 24, 60, 24, 120, 360, 840, 120, 720, 2520, 6720, 15120, 720, 5040, 20160, 60480, 151200, 332640, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200

Offset: 1

Author

Amarnath Murthy, Apr 18 2005

Keywords

• nonn
• tabl

Comments

T(n,n-1)=(2n-1)!/(n-1)! (A000407); T(n,0)=n! (A000142); Row sums yield A092956; Arithmetic means of the rows yield A001761.

Has many diagonals in common with A068424. - Zerinvary Lajos, Apr 14 2006

Examples

			1
2 6
6 24 60
24 120 360 840
120 720 2520 6720 15120
720 5040 20160 60480 151200 332640
5040 40320 181440 604800 1663200 3991680 8648640
40320 362880 1814400 6652800 19958400 51891840 121080960 259459200
		

Crossrefs

Cf. A000407, A000142, A092956, A001761.

Programs

Maple

T:=proc(n,k) if k
				

Formula

T(n, k)=(n+k)!/k! (0<=k<=n-1; n>=1).

Extensions

More terms from Emeric Deutsch, Apr 18 2005