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%I #4 Oct 14 2012 17:35:26
%S 1,1,1,1,1,1,1,1,4,1,10,1,20,1,35,1,56,1,1,84,7,1,120,28,1,165,84,1,
%T 220,210,1,286,462,1,1,364,924,10,1,455,1716,55,1,560,3003,220,1,680,
%U 5005,715,1,816,8008,2002,1
%N Triangle read by rows: T(n,k)=binomial(n-2k,3k) (n>=0, 0<=k<=n/5).
%C Row n contains 1+floor(n/5) terms.
%C Row sums yield A137356.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%p T:=proc(n,k) options operator, arrow: binomial(n-2*k, 3*k) end proc: for n from 0 to 20 do seq(T(n,k),k=0..(1/5)*n) end do; # yields sequence in triangular form
%t Flatten[Table[Binomial[n-2k,3k],{n,0,20},{k,0,Floor[n/5]}]] (* _Harvey P. Dale_, Oct 14 2012 *)
%Y Cf. A137356.
%K nonn,tabf
%O 0,9
%A _Emeric Deutsch_, May 10 2008
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