A112327 Triangle read by rows: T(n,k)=k^3*2^k*binomial(2n-k,n-k)/(2n-k) (1<=k<=n).

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

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.

Links

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

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

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: A097540 A345225 A373997 * A152541 A302339 A361817

Adjacent sequences: A112324 A112325 A112326 * A112328 A112329 A112330

Keyword

nonn,tabl

Author

Emeric Deutsch, Sep 04 2005

Status

approved