A140880 - OEIS

%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