login
Triangle read by rows: T(n,k)=binomial(n-2k,3k+1) (n>=1, 0<=k<=(n-1)/5).
0

%I #4 Aug 12 2018 11:32:24

%S 1,2,3,4,5,6,1,7,5,8,15,9,35,10,70,11,126,1,12,210,8,13,330,36,14,495,

%T 120,15,715,330,16,1001,792,1,17,1365,1716,11,18,1820,3432,66,19,2380,

%U 6435,286,20,3060,11440,1001

%N Triangle read by rows: T(n,k)=binomial(n-2k,3k+1) (n>=1, 0<=k<=(n-1)/5).

%C Row n contains floor((n+4)/5) terms.

%C Row sums yield A137357.

%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+1) end proc: for n to 20 do seq(T(n,k),k=0..(n-1)*1/5) end do; # yields sequence in triangular form

%t Table[Binomial[n-2k,3k+1],{n,30},{k,0,(n-1)/5}]//Flatten (* _Harvey P. Dale_, Aug 12 2018 *)

%Y Cf. A137357.

%K nonn,tabf

%O 1,2

%A _Emeric Deutsch_, May 10 2008