This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A135021 #28 Mar 02 2024 12:00:54
%S A135021 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,
%T A135021 1,1,16807,27951,5915,455,21,1,1,1,262144,799708,229376,20230,896,28,
%U A135021 1,1,1,4782969,27337500,10946964,1166886,55566,1596,36,1,1,1,100000000,1086190605,618435840,82031250,4429152,131250,2640,45,1,1
%N A135021 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.
%C A135021 T(n,r) is the number of (r-1)-trees on n nodes. - _Andrew Howroyd_, Mar 02 2024
%H A135021 G. C. Greubel, <a href="/A135021/b135021.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A135021 L. W. Beineke and R. E. Pipert, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80120-1">The number of labeled k-dimensional trees</a>, J. Comb. Theory 6 (2) (1969) 200-205, formula (1).
%H A135021 Jian-fang Wang and Hai-zhu Li, <a href="http://166.111.121.20:9218/fedora/get/mathjourpaper:YISY200202003/fedora-system:3/getItem?itemID=DS1">Enumeration of Maximum Acyclic Hypergraphs</a>, Acta Mathematicae Applicatae Sinica, English Series, 2002 vol.18 number 2, page 215. [Broken link]
%F A135021 T(n,r) = binomial(n,r-1)*(n*(r-1)-r^2+2*r)^(n-r-1).
%e A135021 From _Bruno Berselli_, Dec 08 2012: (Start)
%e A135021 Triangle begins:
%e A135021 1;
%e A135021 1, 1;
%e A135021 1, 1, 1;
%e A135021 1, 3, 1, 1;
%e A135021 1, 16, 6, 1, 1;
%e A135021 1, 125, 70, 10, 1, 1;
%e A135021 1, 1296, 1215, 200, 15, 1, 1;
%e A135021 1, 16807, 27951, 5915, 455, 21, 1, 1;
%e A135021 1, 262144, 799708, 229376, 20230, 896, 28, 1, 1;
%e A135021 1, 4782969, 27337500, 10946964, 1166886, 55566, 1596, 36, 1, 1;
%e A135021 (End)
%p A135021 seq(seq(binomial(n,r-1)*(n*(r-1)-r^2+2*r)^(n-r-1),r=1..n),n=1..11);
%t A135021 T[n_, r_] := Binomial[n, r - 1]*(n (r - 1) - r^2 + 2 r)^(n - r - 1);
%t A135021 Table[T[n, r], {n, 1, 5}, {r, 1, n}] (* _G. C. Greubel_, Sep 16 2016 *)
%o A135021 (PARI) T(n,r) = binomial(n,r-1)*(n*(r-1)-r^2+2*r)^(n-r-1) \\ _Andrew Howroyd_, Mar 02 2024
%Y A135021 Columns 1..5 are A000012, A000272, A036361, A036362, A036506.
%Y A135021 Cf. A370770 (unlabeled version).
%K A135021 easy,nonn,tabl
%O A135021 0,8
%A A135021 John Nnamdi (john_info_2008(AT)bbvczx.com), Feb 10 2008
%E A135021 Diagonal r=n+1 inserted by _Andrew Howroyd_, Mar 02 2024