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%I #17 Sep 08 2022 08:46:16
%S 1,3,3,15,20,15,84,126,126,84,495,792,924,792,495,3003,5005,6435,6435,
%T 5005,3003,18564,31824,43758,48620,43758,31824,18564,116280,203490,
%U 293930,352716,352716,293930,203490,116280,735471,1307504,1961256,2496144,2704156,2496144,1961256,1307504,735471
%N Triangle read by rows, T(n,k) = binomial(3*n,n+k) for n>=0 and 0<=k<=n.
%H Felix Fröhlich, <a href="/A269956/b269956.txt">Table of n, a(n) for n = 0..10000</a>
%F T(n,0) = T(n,n) = A005809(n).
%e Triangle starts:
%e 1,
%e 3, 3,
%e 15, 20, 15,
%e 84, 126, 126, 84,
%e 495, 792, 924, 792, 495,
%e 3003, 5005, 6435, 6435, 5005, 3003
%p for n from 0 to 6 do seq(binomial(3*n,n+k), k=0..n) od;
%t Table[Binomial[3 n, n + k], {n, 0, 10}, {k, 0, n}]//Flatten (* _Vincenzo Librandi_, Mar 28 2016 *)
%o (Magma) /* As triangle */ [[Binomial(3*n, n+k): k in [0..n]]: n in [0.. 7]]; // _Vincenzo Librandi_, Mar 28 2016
%o (PARI) t(n, k) = binomial(3*n, n+k)
%o trianglerows(n) = for(x=0, n-1, for(y=0, x, print1(t(x, y), ", ")); print(""))
%o /* The following function call prints the upper six rows of the triangle */
%o trianglerows(6) \\ _Felix Fröhlich_, Mar 28 2016
%Y Cf. binomial(m*n,n+k): A000007 (m=0), A010054 (m=1), A094527 (m=2).
%Y Cf. A005809.
%K nonn,tabl
%O 0,2
%A _Peter Luschny_, Mar 28 2016
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