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A193636 Triangle: T(n,k) = C(3n-2k,k), 0 <= k <= n.

%I A193636 #20 Apr 26 2024 09:05:14
%S A193636 1,1,1,1,4,1,1,7,10,1,1,10,28,20,1,1,13,55,84,35,1,1,16,91,220,210,56,
%T A193636 1,1,19,136,455,715,462,84,1,1,22,190,816,1820,2002,924,120,1,1,25,
%U A193636 253,1330,3876,6188,5005,1716,165,1,1,28,325,2024,7315,15504,18564
%N A193636 Triangle: T(n,k) = C(3n-2k,k), 0 <= k <= n.
%H A193636 Robert Israel, <a href="/A193636/b193636.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)
%F A193636 T(n,k) = C(3n-2k,k), 0 <= k <= n.
%F A193636 G.f. as triangle: (1-x*y)^2/(1 - x - 3*x*y + 3*x^2*y^2 - x^3*y^3). - _Robert Israel_, Nov 06 2018
%F A193636 T(n,k) = A102547(3*n,k). - _R. J. Mathar_, Apr 26 2024
%e A193636 First 5 rows:
%e A193636   1;
%e A193636   1,  1;
%e A193636   1,  4,  1;
%e A193636   1,  7, 10,  1;
%e A193636   1, 10, 28, 20,  1; [Corrected by _Robert Israel_, Nov 06 2018]
%p A193636 seq(seq(binomial(3*n-2*k,k),k=0..n),n=0..10); # _Robert Israel_, Nov 06 2018
%t A193636 p[n_, k_] := Binomial[3 n - 2 k, k];
%t A193636 Table[p[n, k], {n, 0, 9}, {k, 0, n}]  (* A193636 *)
%t A193636 Flatten[%]
%o A193636 (Magma) /* As triangle */[[Binomial(3*n-2*k,k): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Nov 07 2018
%Y A193636 Cf. A193635.
%K A193636 nonn,tabl
%O A193636 0,5
%A A193636 _Clark Kimberling_, Aug 01 2011