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%I M1198 #72 Apr 07 2023 12:21:25
%S 1,1,1,2,4,9,27,81,256,1024,4096,16384,78125,390625,1953125,10077696,
%T 60466176,362797056,2176782336,13841287201,96889010407,678223072849,
%U 4747561509943,35184372088832,281474976710656,2251799813685248
%N a(n) = max_{k=0..n} k^(n-k).
%C For n > 0, a(n+1) = largest term of row n in triangles A051129 and A247358. - _Reinhard Zumkeller_, Sep 14 2014
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D I. Tomescu, Introducere in Combinatorica. Editura Tehnica, Bucharest, 1972, p. 231.
%H Seiichi Manyama, <a href="/A003320/b003320.txt">Table of n, a(n) for n = 0..599</a> (terms 0..100 from T. D. Noe).
%H D. Easdown, <a href="http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2015/easdown-19.pdf">Minimal faithful permutation and transformation representations of groups and semigroups</a>, Contemporary Math. (1992), Vol. 131 (Part 3), 75-84.
%H R. Gray and J. D. Mitchell, <a href="http://dx.doi.org/10.1016/j.disc.2007.08.075">Largest subsemigroups of the full transformation monoid</a>, Discrete Math., 308 (2008), 4801-4810.
%H W. S. Gray and M. Thitsa, <a href="https://doi.org/10.1109/SSST.2013.6524939">System Interconnections and Combinatorial Integer Sequences</a>, in: System Theory (SSST), 2013 45th Southeastern Symposium on, Date of Conference: 11-11 March 2013, Digital Object Identifier: 10.1109/SSST.2013.6524939.
%H R. K. Guy, <a href="/A003320/a003320.pdf">Letter to N. J. A. Sloane, Mar 1974</a>
%H I. Tomescu, <a href="/A003320/a003320_4.pdf">Excerpts from "Introducese in Combinatorica" (1972)</a>, pp. 230-1, 44-5, 128-9. (Annotated scanned copy)
%F a(n) = A056155(n-1)^(n - A056155(n-1)), for n >= 2. - _Ridouane Oudra_, Dec 09 2020
%e a(5) = max(5^0, 4^1, 3^2, 2^3, 1^4, 0^5) = max(1,4,9,8,1,0) = 9.
%t Join[{1},Max[#]&/@Table[k^(n-k),{n,25},{k,n}]] (* _Harvey P. Dale_, Jun 20 2011 *)
%o (Haskell)
%o a003320 n = maximum $ zipWith (^) [0 .. n] [n, n-1 ..]
%o -- _Reinhard Zumkeller_, Jun 24 2013
%o (PARI) a(n) = vecmax(vector(n+1, k, (k-1)^(n-k+1))); \\ _Michel Marcus_, Jun 13 2017
%Y Cf. A003992, A031435, A056155.
%K nonn,easy,nice
%O 0,4
%A _N. J. A. Sloane_, _R. K. Guy_
%E Easdown reference from Michail Kats (KatsMM(AT)info.sgu.ru)
%E More terms from _James A. Sellers_, Aug 21 2000
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