%I
%S 1,4,10,20,35,56,2,84,14,120,56,165,168,220,420,286,924,3,364,1848,30,
%T 455,3432,165,560,6006,660,680,10010,2145,816,16016,6006,4,969,24752,
%U 15015,52,1140,37128,34320,364
%N Triangle read by rows: T(n,k)=k*binomial(n2k,3k) (n>=5, 1<=k<=n/5).
%C Row n contains floor(n/5) terms.
%C Row sums yield A137359.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%p T:=proc(n,k) options operator, arrow: k*binomial(n2*k,3*k) end proc: for n from 5 to 22 do seq(T(n,k),k=1..(1/5)*n) end do; # yields sequence in triangular form
%t Flatten[Table[k*Binomial[n2k,3k],{n,5,30},{k,1,n/5}]] (* _Harvey P. Dale_, Dec 20 2014 *)
%Y Cf. A137359.
%K nonn,tabf
%O 5,2
%A _Emeric Deutsch_, May 10 2008
