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%I #12 Jun 25 2018 02:56:42
%S 1,1,3,1,6,12,1,9,33,55,1,12,63,182,273,1,15,102,408,1020,1428,1,18,
%T 150,760,2565,5814,7752,1,21,207,1265,5313,15939,33649,43263,1,24,273,
%U 1950,9750,35880,98670,197340,246675,1,27,348,2842,16443,71253,237510
%N Triangle read by rows: T(n,k) = binomial(3n+3, k)*(n-k+1)/(n+1).
%H Harry J. Smith, <a href="/A064282/b064282.txt">Table of n, a(n) for n = 0..1000</a>
%F T(n, k) = T(n-1, k) + 3*T(n-1, k-1) + 3*T(n-1, k-2) + T(n-1, k-3) [starting with T(0,0)=1 and T(n,k)=0 if n < 0 or n < k].
%t Flatten[Table[Binomial[3n+3,k] (n-k+1)/(n+1),{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Dec 26 2014 *)
%o (PARI) { n=-1; for (m=0, 10^9, for (k=0, m, a=binomial(3*m + 3, k)*(m - k + 1)/(m + 1); write("b064282.txt", n++, " ", a); if (n==1000, break)); if (n==1000, break) ) } \\ _Harry J. Smith_, Sep 11 2009
%Y Columns include A000012 and A008585. Right hand columns include A001764 and A006630. Row sums are A047099. Triangles A010054 (Triangle Indicator), A007318 (Pascal) and A050166 form a sequence which has this as its next member.
%K nonn,tabl
%O 0,3
%A _Henry Bottomley_, Sep 24 2001
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