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

%I A105725 #5 Dec 05 2013 19:57:00
%S A105725 1,2,6,6,24,60,24,120,360,840,120,720,2520,6720,15120,720,5040,20160,
%T A105725 60480,151200,332640,5040,40320,181440,604800,1663200,3991680,8648640,
%U A105725 40320,362880,1814400,6652800,19958400,51891840,121080960,259459200
%N A105725 Triangle read by rows: T(n,k)=(n+k)!/k! (0<=k<=n-1; n>=1).
%C A105725 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.
%C A105725 Has many diagonals in common with A068424. - _Zerinvary Lajos_, Apr 14 2006
%F A105725 T(n, k)=(n+k)!/k! (0<=k<=n-1; n>=1).
%e A105725 1
%e A105725 2 6
%e A105725 6 24 60
%e A105725 24 120 360 840
%e A105725 120 720 2520 6720 15120
%e A105725 720 5040 20160 60480 151200 332640
%e A105725 5040 40320 181440 604800 1663200 3991680 8648640
%e A105725 40320 362880 1814400 6652800 19958400 51891840 121080960 259459200
%p A105725 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
%Y A105725 Cf. A000407, A000142, A092956, A001761.
%K A105725 nonn,tabl
%O A105725 1,2
%A A105725 _Amarnath Murthy_, Apr 18 2005
%E A105725 More terms from _Emeric Deutsch_, Apr 18 2005