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A112326 Triangle read by rows: T(n,k)=2^k*binomial(2n-k,n-k), 1<=k<=n. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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).

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

LINKS

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

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

CROSSREFS

Cf. A068551, A000984.

Sequence in context: A299822 A052100 A079579 * A075435 A069875 A202962

Adjacent sequences:  A112323 A112324 A112325 * A112327 A112328 A112329

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Sep 04 2005

STATUS

approved

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Last modified June 24 09:37 EDT 2019. Contains 324323 sequences. (Running on oeis4.)