A152168 -id:A152168 - cp's OEIS frontend

A000197 a(n) = (n!)!.

1, 1, 2, 720, 620448401733239439360000

Offset: 0

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

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).

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

Cf. A063979. - Robert G. Wilson v, Dec 04 2008
Cf. A152168. - Alois P. Heinz, Aug 04 2013
Cf. A000142, A006990, A245087.

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

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

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

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

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

A348651 Number of ones in the binary expansion of (n!)!.

Original entry on oeis.org

1, 1, 1, 4, 29, 293, 2566, 24844, 259437, 2908263, 35102629, 455204360, 6321171774

Offset: 0

Alois P. Heinz, Oct 27 2021

			a(3) = 4 because (3!)! = 6! = 720 = 1011010000_2 which has 4 ones.

Index entries for sequences related to factorial numbers

Cf. A000120, A000142, A000197, A079584, A152168, A301861.

a:= n-> add(i, i=Bits[Split](n!!)):
seq(a(n), n=0..10);

a[n_] := DigitCount[(n!)!, 2, 1]; Array[a, 10, 0] (* Amiram Eldar, Oct 29 2021 *)

a(n) = hammingweight((n!)!); \\ Michel Marcus, Oct 29 2021

from gmpy2 import fac, popcount
def A348651(n): return popcount(fac(fac(n))) # Chai Wah Wu, Oct 28 2021

a(n) = A000120(A000197(n)).

a(11)-a(12) from Chai Wah Wu, Oct 28 2021

cp's OEIS Frontend

A000197 a(n) = (n!)!.

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