

A000197


a(n) = (n!)!.
(Formerly M2187 N0874)


17




OFFSET

0,3


COMMENTS

The sequence 1, 2, 720!, 4!!!!, ... ,n!!...! (n times) grows too rapidly to have its own entry. See Hofstadter.
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
See bfile for a(5), which has 199 digits and is too large to include.  Jianing Song, Jun 28 2018


REFERENCES

Archimedeans Problems Drive, Eureka, 37 (1974), 11.
Douglas R. Hofstadter, Fluid concepts & creative analogies: computer models of the fundamental mechanisms of thought, Basic Books, 1995, pages 4446. [From Colin Rowat, Sep 30 2011]
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Franklin T. AdamsWatters, Table of n, a(n) for n=0..5
R. Ondrejka, 1273 exact factorials, Math. Comp., 24 (1970), 231.
Eric Weisstein's World of Mathematics, Factorial
Index entries for sequences related to factorial numbers


FORMULA

a(n) = A000142(A000142(n)).  Wesley Ivan Hurt, Jul 14 2014


MAPLE

A000197:=n>(n!)!: seq(A000197(n), n=0..5); # Wesley Ivan Hurt, Jul 14 2014


MATHEMATICA

Table[(n!)!, {n, 0, 5}] (* Wesley Ivan Hurt, Jul 14 2014 *)


PROG

(MAGMA) [Factorial(Factorial(n)) : n in [0..5]]; // Wesley Ivan Hurt, Jul 14 2014


CROSSREFS

Cf. A063979.  Robert G. Wilson v, Dec 04 2008
Cf. A152168.  Alois P. Heinz, Aug 04 2013
Cf. A000142, A006990, A245087.
Sequence in context: A185667 A119781 A028367 * A036298 A341078 A153923
Adjacent sequences: A000194 A000195 A000196 * A000198 A000199 A000200


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



