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

1,1

Comments

Row sums yield A068551.

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

References

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

Links

Table of n, a(n) for n=1..47.

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

Example

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

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 *)

Crossrefs

Cf. A068551, A000984.

Sequence in context: A052100 A079579 A309243 * A075435 A069875 A202962

Adjacent sequences: A112323 A112324 A112325 * A112327 A112328 A112329

Keyword

nonn,tabl

Author

Emeric Deutsch, Sep 04 2005

Status

approved