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A135021 Triangle read by rows: T(n,r) = number of maximum r-uniform acyclic hypergraphs of order n and size n-r+1. 2
1, 1, 1, 1, 3, 1, 1, 16, 6, 1, 1, 125, 70, 10, 1, 1, 1296, 1215, 200, 15, 1, 1, 16807, 27951, 5915, 455, 21, 1, 1, 262144, 799708, 229376, 20230, 896, 28, 1, 1, 4782969, 27337500, 10946964, 1166886, 55566, 1596, 36, 1, 1, 100000000, 1086190605, 618435840, 82031250, 4429152, 131250, 2640, 45, 1, 1, 2357947691, 49162945645, 40283203125, 6768679170, 426666702, 13763442, 277530, 4125, 55, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows

L. W. Beineke, R. E. Pipert, The number of labeled k-dimensional trees, J. Comb. Theory 6 (2) (1969) 200-205, formula (1).

Wang, Jian-fang and Li, Hai-zhu, Enumeration of Maximum Acyclic Hypergraphs, Acta Mathematicae Applicatae Sinica,English Series, 2002 vol.18 number 2, page 215.

FORMULA

T(n,r) = C(n,r-1)*(n(r-1)-r^2+2r)^(n-r-1).

EXAMPLE

Triangle begins:

1,

1, 1;

1, 3, 1;

1, 16, 6, 1;

1, 125, 70, 10, 1;

1, 1296, 1215, 200, 15, 1;

1, 16807, 27951, 5915, 455, 21, 1;

1, 262144, 799708, 229376, 20230, 896, 28, 1;

1, 4782969, 27337500, 10946964, 1166886, 55566, 1596, 36, 1, etc.

[Bruno Berselli, Dec 08 2012]

MAPLE

seq(seq(binomial(n, r-1)*(n*(r-1)-r^2+2*r)^(n-r-1), r=1..n), n=1..11);

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A156690 A228900 A060325 * A087987 A290311 A322790

Adjacent sequences:  A135018 A135019 A135020 * A135022 A135023 A135024

KEYWORD

easy,nonn,tabl

AUTHOR

John Nnamdi (john_info_2008(AT)bbvczx.com), Feb 10 2008

STATUS

approved

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Last modified August 7 15:30 EDT 2020. Contains 336276 sequences. (Running on oeis4.)