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A112327 Triangle read by rows: T(n,k)=k^3*2^k*binomial(2n-k,n-k)/(2n-k) (1<=k<=n). 1
2, 2, 16, 4, 32, 72, 10, 80, 216, 256, 28, 224, 648, 1024, 800, 84, 672, 2016, 3584, 4000, 2304, 264, 2112, 6480, 12288, 16000, 13824, 6272, 858, 6864, 21384, 42240, 60000, 62208, 43904, 16384, 2860, 22880, 72072, 146432, 220000, 253440, 219520, 131072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

T(n,1)=2*Catalan(n-1)=2*A000108(n-1) T(n,n)=2^n*n^2=A007758(n). Row sums yield A112328.

REFERENCES

F. Ruskey, Average shape of binary trees, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50 (Eq. (8)).

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

Triangle starts:

2;

2,16;

4,32,72;

10,80,216,256;

MAPLE

T:=proc(n, k) if k<2*n then k^3*2^k*binomial(2*n-k, n-k)/(2*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. A000108, A007758, A112328.

Sequence in context: A184718 A079897 A097540 * A152541 A302339 A093114

Adjacent sequences:  A112324 A112325 A112326 * A112328 A112329 A112330

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Sep 04 2005

STATUS

approved

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Last modified June 16 10:03 EDT 2019. Contains 324152 sequences. (Running on oeis4.)