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A135021
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Triangle read by rows: T(n,r) = number of maximum r-uniform acyclic hypergraphs of order n and size n-r+1, 1 <= r <= n+1.
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6
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1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 16, 6, 1, 1, 1, 125, 70, 10, 1, 1, 1, 1296, 1215, 200, 15, 1, 1, 1, 16807, 27951, 5915, 455, 21, 1, 1, 1, 262144, 799708, 229376, 20230, 896, 28, 1, 1, 1, 4782969, 27337500, 10946964, 1166886, 55566, 1596, 36, 1, 1, 1, 100000000, 1086190605, 618435840, 82031250, 4429152, 131250, 2640, 45, 1, 1
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OFFSET
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0,8
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COMMENTS
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T(n,r) is the number of (r-1)-trees on n nodes. - Andrew Howroyd, Mar 02 2024
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LINKS
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FORMULA
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T(n,r) = binomial(n,r-1)*(n*(r-1)-r^2+2*r)^(n-r-1).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 1, 1;
1, 3, 1, 1;
1, 16, 6, 1, 1;
1, 125, 70, 10, 1, 1;
1, 1296, 1215, 200, 15, 1, 1;
1, 16807, 27951, 5915, 455, 21, 1, 1;
1, 262144, 799708, 229376, 20230, 896, 28, 1, 1;
1, 4782969, 27337500, 10946964, 1166886, 55566, 1596, 36, 1, 1;
(End)
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MAPLE
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seq(seq(binomial(n, r-1)*(n*(r-1)-r^2+2*r)^(n-r-1), r=1..n), n=1..11);
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MATHEMATICA
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T[n_, r_] := Binomial[n, r - 1]*(n (r - 1) - r^2 + 2 r)^(n - r - 1);
Table[T[n, r], {n, 1, 5}, {r, 1, n}] (* G. C. Greubel, Sep 16 2016 *)
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PROG
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(PARI) T(n, r) = binomial(n, r-1)*(n*(r-1)-r^2+2*r)^(n-r-1) \\ Andrew Howroyd, Mar 02 2024
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CROSSREFS
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KEYWORD
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AUTHOR
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John Nnamdi (john_info_2008(AT)bbvczx.com), Feb 10 2008
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EXTENSIONS
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STATUS
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approved
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