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

1,2

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

Links

Table of n, a(n) for n=1..36.

Formula

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

Example

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

Maple

T:=proc(n, k) if k<n then (n+k)!/k! else 0 fi end: for n from 1 to 9 do seq(T(n, k), k=0..n-1) od; # yields sequence in triangular form

Crossrefs

Cf. A000407, A000142, A092956, A001761.

Sequence in context: A130865 A327630 A282170 * A005226 A087310 A130087

Adjacent sequences: A105722 A105723 A105724 * A105726 A105727 A105728

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 18 2005

Extensions

More terms from Emeric Deutsch, Apr 18 2005

Status

approved