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A000197
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a(n) = (n!)!.
(Formerly M2187 N0874)
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17
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OFFSET
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0,3
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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Franklin T. Adams-Watters, 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
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FORMULA
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a(n) = A000142(A000142(n)). - Wesley Ivan Hurt, Jul 14 2014
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MAPLE
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A000197:=n->(n!)!: seq(A000197(n), n=0..5); # Wesley Ivan Hurt, Jul 14 2014
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MATHEMATICA
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Table[(n!)!, {n, 0, 5}] (* Wesley Ivan Hurt, Jul 14 2014 *)
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PROG
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(MAGMA) [Factorial(Factorial(n)) : n in [0..5]]; // Wesley Ivan Hurt, Jul 14 2014
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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