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%I #7 Sep 20 2019 04:51:00
%S 2,6,4,20,16,8,70,60,40,16,252,224,168,96,32,924,840,672,448,224,64,
%T 3432,3168,2640,1920,1152,512,128,12870,12012,10296,7920,5280,2880,
%U 1152,256,48620,45760,40040,32032,22880,14080,7040,2560,512,184756,175032
%N Triangle read by rows: T(n,k)=2^k*binomial(2n-k,n-k), 1<=k<=n.
%C Row sums yield A068551.
%C T(n,1) = binomial(2n,n) = A000984(n); T(n,n) = 2^n.
%D M. Eisen, Elementary Combinatorial Analysis, Gordon and Breach, 1969 (p. 150).
%H F. Ruskey, <a href="https://doi.org/10.1137/0601007">Average shape of binary trees</a>, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50.
%e Triangle starts:
%e 2;
%e 6,4;
%e 20,16,8;
%e 70,60,40,16;
%p T:=proc(n,k) if k<=n then 2^k*binomial(2*n-k,n-k) else 0 fi end: for n from 1 to 10 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form
%t Flatten[Table[2^k*Binomial[2n-k,n-k],{n,1,10},{k,1,n}]] (* _Stefano Spezia_, Sep 20 2019 *)
%Y Cf. A068551, A000984.
%K nonn,tabl
%O 1,1
%A _Emeric Deutsch_, Sep 04 2005
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