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A301861
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a(n) is the sum of the decimal digits of (n!)!.
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2
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1, 1, 2, 9, 81, 783, 7164, 69048, 711009, 7961040, 95935761, 1242436185, 17235507996
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OFFSET
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0,3
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COMMENTS
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Presumably, lim_{n->oo} a(n)/A008906(n!) = 9/2.
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LINKS
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FORMULA
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EXAMPLE
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a(0) = digitsum((0!)!) = digitsum(1!) = digitsum(1) = 1.
a(1) = digitsum((1!)!) = digitsum(1!) = digitsum(1) = 1.
a(2) = digitsum((2!)!) = digitsum(2!) = digitsum(2) = 2.
a(3) = digitsum((3!)!) = digitsum(6!) = digitsum(720) = 7+2 = 9.
a(4) = digitsum((4!)!) = digitsum(24!) = digitsum(620448401733239439360000) = 6+2+0+4+4+8+4+0+1+7+3+3+2+3+9+4+3+9+3+6+0+0+0+0 = 81.
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MAPLE
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a:= n-> add(i, i=convert(n!!, base, 10)):
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MATHEMATICA
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PROG
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(Magma) [&+Intseq(Factorial(Factorial(n))): n in [0..10]]; // Vincenzo Librandi, Mar 29 2018
(Python)
from math import factorial
return sum(int(d) for d in str(factorial(factorial(n)))) # Chai Wah Wu, Mar 31 2018
# faster program for larger values of n
from gmpy2 import mpz, digits, fac
def A301861(n): return int(sum(mpz(d) for d in digits(fac(fac(n))))) # Chai Wah Wu, Oct 24 2021
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CROSSREFS
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Cf. A000142 (factorial numbers), A000197 ((n!)!), A004152 (sum of digits of n!), A007953 (sum of digits of n), A008906 (number of digits in n! excluding trailing zeros), A027868 (number of trailing zeros in n!), A034886 (number of digits in n!), A063979 (number of digits in (n!)!).
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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