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A105725 Triangle read by rows: T(n,k)=(n+k)!/k! (0<=k<=n-1; n>=1). 3
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 (list; table; graph; refs; listen; history; text; internal format)
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: A100634 A242527 A130865 * 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

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Last modified October 1 14:30 EDT 2014. Contains 247511 sequences.