A112326 Triangle read by rows: T(n,k)=2^k*binomial(2n-k,n-k), 1<=k<=n.

2, 6, 4, 20, 16, 8, 70, 60, 40, 16, 252, 224, 168, 96, 32, 924, 840, 672, 448, 224, 64, 3432, 3168, 2640, 1920, 1152, 512, 128, 12870, 12012, 10296, 7920, 5280, 2880, 1152, 256, 48620, 45760, 40040, 32032, 22880, 14080, 7040, 2560, 512, 184756, 175032

Offset: 1

Author

Emeric Deutsch, Sep 04 2005

Keywords

• nonn
• tabl

Comments

Row sums yield A068551.

T(n,1) = binomial(2n,n) = A000984(n); T(n,n) = 2^n.

Examples

			Triangle starts:
2;
6,4;
20,16,8;
70,60,40,16;
		

References

• M. Eisen, Elementary Combinatorial Analysis, Gordon and Breach, 1969 (p. 150).

Links

• F. Ruskey, Average shape of binary trees, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50.

Crossrefs

Cf. A068551, A000984.

Programs

Maple

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

Mathematica

Flatten[Table[2^k*Binomial[2n-k,n-k],{n,1,10},{k,1,n}]] (* Stefano Spezia, Sep 20 2019 *)