A000197 a(n) = (n!)!. (Formerly M2187 N0874)

1, 1, 2, 720, 620448401733239439360000

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 b-file 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 44-46. [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. Adams-Watters, Table of n, a(n) for n=0..5

Rudolph 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

Sum_{n>=0} 1/a(n) = A336686. - Amiram Eldar, Mar 10 2021

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: A119781 A362187 A028367 * A036298 A341078 A153923

Adjacent sequences: A000194 A000195 A000196 * A000198 A000199 A000200

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved