A003320 a(n) = max_{k=0..n} k^(n-k). (Formerly M1198)

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

0,4

Comments

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

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)

Formula

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

Example

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

Mathematica

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

Prog

(Haskell)
a003320 n = maximum $ zipWith (^) [0 .. n] [n, n-1 ..]
-- Reinhard Zumkeller, Jun 24 2013
(PARI) a(n) = vecmax(vector(n+1, k, (k-1)^(n-k+1))); \\ Michel Marcus, Jun 13 2017

Crossrefs

Cf. A003992, A031435, A056155.

Sequence in context: A359502 A110138 A148085 * A007876 A343845 A349404

Adjacent sequences: A003317 A003318 A003319 * A003321 A003322 A003323

Keyword

nonn,easy,nice

Author

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

Extensions

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

More terms from James A. Sellers, Aug 21 2000

Status

approved