A097547 a(n) = n^(2^n).

0, 1, 16, 6561, 4294967296, 23283064365386962890625, 63340286662973277706162286946811886609896461828096, 1487815647197611695910312681741273570332356717154798949898498305086387315423300999654757561928633305897036801

Offset: 0

Author

Yasutoshi Kohmoto, Aug 28 2004

Keywords

• nonn

Comments

Number of mappings from 2^X to X where X is an n-set.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..9 (shortened by _N. J. A. Sloane_, Jan 13 2019)
• Yasutoshi Kohmoto, The Other Side of Mathematics [broken link?]
• Yasutoshi Kohmoto, The Other Side of Mathematics [via Internet Archive Wayback-machine]

Crossrefs

Cf. A000290, A020955, A099129, A216992.

Programs

Magma

[n^(2^n): n in [0..12]]; // Vincenzo Librandi, May 25 2011

Maple

a:= n-> (t-> (t@@n)(n))(j-> j^2):
seq(a(n), n=0..7);  # Alois P. Heinz, Sep 29 2023

Mathematica

Table[n^2^n,{n,0,7}] (* Vladimir Joseph Stephan Orlovsky, Mar 01 2010 *)

PARI

a(n)=n^(1<Charles R Greathouse IV, May 25 2011

Formula

From R. J. Mathar, Apr 23 2007: (Start)

a(6) = A080174(6) - 1.

a(5) = A013737(10) = A013835(6).

a(4) = A000079(32) = A002489(4) = A000215(5)-1.

(End)

Sum_{n>=1} 1/a(n) = A216992. - Amiram Eldar, Nov 19 2020