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The largest number that can be written with n characters, using positive integers, exponentiation and the factorial function.
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%I #12 Feb 22 2019 02:08:36

%S 9,387420489

%N The largest number that can be written with n characters, using positive integers, exponentiation and the factorial function.

%C The sequence is infinite, but cannot be displayed in OEIS format after a(2).

%H Daniel J. Velleman, <a href="http://www.jstor.org/stable/27642031">Exponential vs. Factorial</a>, Am. Math. Monthly, Vol. 113, No.8, pp. 689-703, Oct 2006.

%F For n > 2, Velleman proves that a(n+1) = a(n)!.

%e a(1) = 9, as we are writing in base 10.

%e a(2) = 9^9 = 387420489, when writing exponentiation with superscripting instead of using the character "^".

%K nonn,base,bref

%O 1,1

%A _Jonathan Vos Post_, Jan 04 2009