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%I #5 Mar 30 2012 18:57:38
%S 1,1,2,1,5,6,1,8,21,20,1,11,45,84,70,1,14,78,220,330,252,1,17,120,455,
%T 1001,1287,924,1,20,171,816,2380,4368,5005,3432,1,23,231,1330,4845,
%U 11628,18564,19448,12870,1,26,300,2024,8855,26334,54264,77520,75582
%N Triangle: T(n,k)=C(3n-k,k), 0<=k<=n.
%F T(n,k)=C(3n-k,k), 0<=k<=n.
%e First 5 rows of A193635:
%e 1
%e 1...2
%e 1...7....10
%e 1...15...66....82
%e 1...26...231...811...930
%t p[n_, k_] := Binomial[3 n - k, k];
%t Table[p[n, k], {n, 0, 9}, {k, 0, n}] (* A193635 *)
%t Flatten[%]
%Y Cf. A193636.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Aug 01 2011
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