This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140880 #12 Oct 29 2017 14:20:40
%S A140880 2,6,6,12,24,12,20,60,60,20,30,120,180,120,30,42,210,420,420,210,42,
%T A140880 56,336,840,1120,840,336,56,72,504,1512,2520,2520,1512,504,72,90,720,
%U A140880 2520,5040,6300,5040,2520,720,90
%N A140880 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 A140880 Triangle starts:
%e A140880 [0] 2
%e A140880 [1] 6, 6
%e A140880 [2] 12, 24, 12
%e A140880 [3] 20, 60, 60, 20
%e A140880 [4] 30, 120, 180, 120, 30
%e A140880 [5] 42, 210, 420, 420, 210, 42
%e A140880 [6] 56, 336, 840, 1120, 840, 336, 56
%e A140880 [7] 72, 504, 1512, 2520, 2520, 1512, 504, 72
%e A140880 [8] 90, 720, 2520, 5040, 6300, 5040, 2520, 720, 90
%p A140880 T := (n,k) -> GAMMA(n+3)/(GAMMA(k+1)*GAMMA(n-k+1)):
%p A140880 seq(seq(T(n,k), k=0..n), n=0..8); # _Peter Luschny_, Oct 29 2017
%t A140880 Flatten[Table[Gamma[n+3]/(Gamma[k+1]Gamma[n-k+1]),{n,0,8},{k,0,n}]]
%Y A140880 T(n,0) = T(n,n) = A002378(n+1). T(n,k) = 2*A094305(n,k).
%Y A140880 Row sums are A001815(n+2).
%Y A140880 Cf. A007318.
%K A140880 nonn,tabl
%O A140880 0,1
%A A140880 _Roger L. Bagula_ and _Gary W. Adamson_, Jul 22 2008
%E A140880 Edited and new name from _Peter Luschny_, Oct 29 2017