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%I #12 Oct 29 2017 14:20:40
%S 2,6,6,12,24,12,20,60,60,20,30,120,180,120,30,42,210,420,420,210,42,
%T 56,336,840,1120,840,336,56,72,504,1512,2520,2520,1512,504,72,90,720,
%U 2520,5040,6300,5040,2520,720,90
%N Triangle read by rows, T(n,k) = Gamma(n+3)/(Gamma(k+1)*Gamma(n-k+1)) for n>=0 and 0<=k<=n.
%e Triangle starts:
%e [0] 2
%e [1] 6, 6
%e [2] 12, 24, 12
%e [3] 20, 60, 60, 20
%e [4] 30, 120, 180, 120, 30
%e [5] 42, 210, 420, 420, 210, 42
%e [6] 56, 336, 840, 1120, 840, 336, 56
%e [7] 72, 504, 1512, 2520, 2520, 1512, 504, 72
%e [8] 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90
%p T := (n,k) -> GAMMA(n+3)/(GAMMA(k+1)*GAMMA(n-k+1)):
%p seq(seq(T(n,k), k=0..n), n=0..8); # _Peter Luschny_, Oct 29 2017
%t Flatten[Table[Gamma[n+3]/(Gamma[k+1]Gamma[n-k+1]),{n,0,8},{k,0,n}]]
%Y T(n,0) = T(n,n) = A002378(n+1). T(n,k) = 2*A094305(n,k).
%Y Row sums are A001815(n+2).
%Y Cf. A007318.
%K nonn,tabl
%O 0,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 22 2008
%E Edited and new name from _Peter Luschny_, Oct 29 2017
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