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A112327
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Triangle read by rows: T(n,k)=k^3*2^k*binomial(2n-k,n-k)/(2n-k) (1<=k<=n).
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1
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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
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OFFSET
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1,1
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COMMENTS
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T(n,1)=2*Catalan(n-1)=2*A000108(n-1) T(n,n)=2^n*n^2=A007758(n). Row sums yield A112328.
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REFERENCES
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F. Ruskey, Average shape of binary trees, SIAM J. Alg. Disc. Meth., 1, 1980, 43-50 (Eq. (8)).
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LINKS
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Table of n, a(n) for n=1..44.
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EXAMPLE
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Triangle starts:
2;
2,16;
4,32,72;
10,80,216,256;
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MAPLE
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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
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CROSSREFS
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Cf. A000108, A007758, A112328.
Sequence in context: A184718 A079897 A097540 * A152541 A093114 A016740
Adjacent sequences: A112324 A112325 A112326 * A112328 A112329 A112330
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch, Sep 04 2005
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STATUS
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approved
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