A003320 a(n) = max_{k=0..n} k^(n-k).

1, 1, 1, 2, 4, 9, 27, 81, 256, 1024, 4096, 16384, 78125, 390625, 1953125, 10077696, 60466176, 362797056, 2176782336, 13841287201, 96889010407, 678223072849, 4747561509943, 35184372088832, 281474976710656, 2251799813685248

Offset: 0

Author

N. J. A. Sloane, R. K. Guy

Keywords

• nonn
• easy
• nice

Comments

For n > 0, a(n+1) = largest term of row n in triangles A051129 and A247358. - Reinhard Zumkeller, Sep 14 2014

Examples

			a(5) = max(5^0, 4^1, 3^2, 2^3, 1^4, 0^5) = max(1,4,9,8,1,0) = 9.
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• I. Tomescu, Introducere in Combinatorica. Editura Tehnica, Bucharest, 1972, p. 231.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..599 (terms 0..100 from T. D. Noe).
• D. Easdown, Minimal faithful permutation and transformation representations of groups and semigroups, Contemporary Math. (1992), Vol. 131 (Part 3), 75-84.
• R. Gray and J. D. Mitchell, Largest subsemigroups of the full transformation monoid, Discrete Math., 308 (2008), 4801-4810.
• W. S. Gray and M. Thitsa, System Interconnections and Combinatorial Integer Sequences, in: System Theory (SSST), 2013 45th Southeastern Symposium on, Date of Conference: 11-11 March 2013, Digital Object Identifier: 10.1109/SSST.2013.6524939.
• R. K. Guy, Letter to N. J. A. Sloane, Mar 1974
• I. Tomescu, Excerpts from "Introducese in Combinatorica" (1972), pp. 230-1, 44-5, 128-9. (Annotated scanned copy)

Crossrefs

Cf. A003992, A031435, A056155.

Programs

Haskell

a003320 n = maximum $ zipWith (^) [0 .. n] [n, n-1 ..]
-- Reinhard Zumkeller, Jun 24 2013

Mathematica

Join[{1},Max[#]&/@Table[k^(n-k),{n,25},{k,n}]] (* Harvey P. Dale, Jun 20 2011 *)

PARI

a(n) = vecmax(vector(n+1, k, (k-1)^(n-k+1))); \\ Michel Marcus, Jun 13 2017

Formula

a(n) = A056155(n-1)^(n - A056155(n-1)), for n >= 2. - Ridouane Oudra, Dec 09 2020

Extensions

Easdown reference from Michail Kats (KatsMM(AT)info.sgu.ru)

More terms from James Sellers, Aug 21 2000