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a(n) = n^(2^n).
4

%I #37 Sep 29 2023 19:43:32

%S 0,1,16,6561,4294967296,23283064365386962890625,

%T 63340286662973277706162286946811886609896461828096,

%U 1487815647197611695910312681741273570332356717154798949898498305086387315423300999654757561928633305897036801

%N a(n) = n^(2^n).

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

%H Vincenzo Librandi, <a href="/A097547/b097547.txt">Table of n, a(n) for n = 0..9</a> (shortened by _N. J. A. Sloane_, Jan 13 2019)

%H Yasutoshi Kohmoto, <a href="http://boat.zero.ad.jp/~zbi74583/another02.htm">The Other Side of Mathematics</a> [broken link?]

%H Yasutoshi Kohmoto, <a href="http://web.archive.org/web/20120409075427/http://boat.zero.ad.jp/~zbi74583/another02.htm">The Other Side of Mathematics</a> [via Internet Archive Wayback-machine]

%F From _R. J. Mathar_, Apr 23 2007: (Start)

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

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

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

%F (End)

%F Sum_{n>=1} 1/a(n) = A216992. - _Amiram Eldar_, Nov 19 2020

%p a:= n-> (t-> (t@@n)(n))(j-> j^2):

%p seq(a(n), n=0..7); # _Alois P. Heinz_, Sep 29 2023

%t Table[n^2^n,{n,0,7}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 01 2010 *)

%o (Magma) [n^(2^n): n in [0..12]]; // _Vincenzo Librandi_, May 25 2011

%o (PARI) a(n)=n^(1<<n) \\ _Charles R Greathouse IV_, May 25 2011

%Y Cf. A000290, A020955, A099129, A216992.

%K nonn

%O 0,3

%A _Yasutoshi Kohmoto_, Aug 28 2004