|
%I M2187 N0874 #46 Sep 08 2022 08:44:27
%S 1,1,2,720,620448401733239439360000
%N a(n) = (n!)!.
%C The sequence 1, 2, 720!, 4!!!!, ... ,n!!...! (n times) grows too rapidly to have its own entry. See Hofstadter.
%C a(n) is divisible by 2^A245087(n) but not by 2^(A245087(n)+1), A245087 being the number of trailing zeros in its binary expansion. Also, for n>1, the largest prime divisor of a(n) is the largest prime <= n!, which is listed in A006990(n). - _Stanislav Sykora_, Jul 14 2014
%C See b-file for a(5), which has 199 digits and is too large to include. - _Jianing Song_, Jun 28 2018
%D Archimedeans Problems Drive, Eureka, 37 (1974), 11.
%D Douglas R. Hofstadter, Fluid concepts & creative analogies: computer models of the fundamental mechanisms of thought, Basic Books, 1995, pages 44-46. [From Colin Rowat, Sep 30 2011]
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Franklin T. Adams-Watters, <a href="/A000197/b000197.txt">Table of n, a(n) for n=0..5</a>
%H Rudolph Ondrejka, <a href="http://dx.doi.org/10.1090/S0025-5718-70-99856-X">1273 exact factorials</a>, Math. Comp., 24 (1970), 231.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Factorial.html">Factorial</a>.
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F a(n) = A000142(A000142(n)). - _Wesley Ivan Hurt_, Jul 14 2014
%F Sum_{n>=0} 1/a(n) = A336686. - _Amiram Eldar_, Mar 10 2021
%p A000197:=n->(n!)!: seq(A000197(n), n=0..5); # _Wesley Ivan Hurt_, Jul 14 2014
%t Table[(n!)!, {n, 0, 5}] (* _Wesley Ivan Hurt_, Jul 14 2014 *)
%o (Magma) [Factorial(Factorial(n)) : n in [0..5]]; // _Wesley Ivan Hurt_, Jul 14 2014
%Y Cf. A063979. - _Robert G. Wilson v_, Dec 04 2008
%Y Cf. A152168. - _Alois P. Heinz_, Aug 04 2013
%Y Cf. A000142, A006990, A245087.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
| 