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
Examples
Triangle starts: 2; 2,16; 4,32,72; 10,80,216,256;
Links
- F. Ruskey, Average shape of binary trees, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50 (Eq. (8)).
Programs
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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
Comments