%I #4 Aug 22 2015 17:35:36
%S 1,6,21,56,126,252,2,462,18,792,90,1287,330,2002,990,3003,2574,3,4368,
%T 6006,36,6188,12870,234,8568,25740,1092,11628,48620,4095,15504,87516,
%U 13104,4,20349,151164,37128,60
%N Triangle read by rows: T(n,k)=k*binomial(n-2k,3k+2) (n>=7, 1<=k<=(n-2)/5).
%C Row n contains floor((n-2)/5) terms.
%C Row sums yield A137361.
%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(n-2*k, 3*k+2) end proc: for n from 7 to 23 do seq(T(n,k),k=1..(n-2)*1/5) end do; # yields sequence in triangular form
%t Flatten[Table[k*Binomial[n-2k,3k+2],{n,7,30},{k,1,(n-2)/5}]] (* _Harvey P. Dale_, Aug 22 2015 *)
%Y Cf. A137361.
%K nonn,tabf
%O 7,2
%A _Emeric Deutsch_, May 10 2008