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%I A354463 #32 Jun 25 2022 21:44:36
%S A354463 0,0,0,1,3,7,14,31,63,126,253,509,1021,2045,4094,8189,16380,32763,
%T A354463 65531,131067,262140,524285,1048571,2097146,4194297,8388603,16777208,
%U A354463 33554424,67108858,134217720,268435446,536870902,1073741816,2147483642,4294967289,8589934584,17179869176,34359738358,68719476729
%N A354463 a(n) is the number of trailing zeros in (2^n)!.
%H A354463 William Boyles, <a href="/A354463/b354463.txt">Table of n, a(n) for n = 0..650</a>
%F A354463 a(n) = A027868(A000079(n)). - _Michel Marcus_, Jun 01 2022
%F A354463 a(n) = 2^(n-2) - A055223(n) for n >= 2. - _John Keith_, Jun 06 2022
%e A354463 For n = 4, (2^4)! = 20922789888000, which has a(4) = 3 trailing zeros.
%t A354463 a[n_]:=IntegerExponent[(2^n)!]; Array[a,38,0] (* _Stefano Spezia_, Jun 01 2022 *)
%o A354463 (Haskell)
%o A354463 seq n = aux (2 ^ n) 0
%o A354463   where
%o A354463     aux x acc
%o A354463       | x < 5 = acc
%o A354463       | otherwise = aux y (acc + y)
%o A354463       where
%o A354463         y = x `div` 5
%o A354463 (PARI) a(n) = val(1<<n, 5)
%o A354463 val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Jun 01 2022
%o A354463 (Python)
%o A354463 from sympy import factorial, multiplicity
%o A354463 def a(n): return multiplicity(5, factorial(2**n, evaluate=False))
%o A354463 print([a(n) for n in range(39)]) # _Michael S. Branicky_, Jun 01 2022
%o A354463 (Python)
%o A354463 def A354463(n):
%o A354463     c, m = 0, 2**n
%o A354463     while m >= 5:
%o A354463         m //= 5
%o A354463         c += m
%o A354463     return c # _Chai Wah Wu_, Jun 02 2022
%Y A354463 Cf. A000079, A027868.
%K A354463 nonn,easy,base
%O A354463 0,5
%A A354463 _William Boyles_, May 31 2022

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