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A004154
a(n) = n! with trailing zeros omitted.
18
1, 1, 2, 6, 24, 12, 72, 504, 4032, 36288, 36288, 399168, 4790016, 62270208, 871782912, 1307674368, 20922789888, 355687428096, 6402373705728, 121645100408832, 243290200817664, 5109094217170944, 112400072777760768, 2585201673888497664, 62044840173323943936
OFFSET
0,3
FORMULA
a(n) = A000142(n) / 10^A027868(n). - Reinhard Zumkeller, Nov 24 2012
a(n+1) = A004151((n+1)*a(n)). - Reinhard Zumkeller, Nov 24 2012, corrected by M. F. Hasler, Oct 16 2014
a(n) = A004151(A000142(n)) = A000142(n)/A011557(A112765(n)), or A122840 instead of A112765. - M. F. Hasler, Oct 16 2014
MAPLE
a:= n-> (f-> f/10^padic[ordp](f, 10))(n!):
seq(a(n), n=0..29); # Alois P. Heinz, Dec 29 2021
MATHEMATICA
Array[#!//.x_/; x~Mod~5==0:>x/10&, 22] (* Giorgos Kalogeropoulos, Aug 17 2020 *)
Join[{1, 1, 2, 6, 24}, Table[FromDigits[Flatten[Most[Split[IntegerDigits[n!]]]]], {n, 5, 30}]] (* or *) Table[n!/10^IntegerExponent[n!, 10], {n, 0, 30}] (* Harvey P. Dale, Feb 13 2024 *)
PROG
(Haskell)
a004154 = a004151 . a000142
a004154_list = scanl (\u v -> a004151 $ u * v) 1 [1..]
-- Reinhard Zumkeller, Nov 24 2012
(PARI) a(n)=n!/10^valuation(n!, 5) \\ M. F. Hasler, Oct 16 2014
(Magma) [Factorial(n)/10^Valuation(Factorial(n), 5): n in [0..30]]; // Vincenzo Librandi, Oct 16 2014
(Python)
from sympy import factorial
from sympy.ntheory.factor_ import digits
def A004154(n): return factorial(n)//10**(n-sum(digits(n, 5)[1:])>>2) # Chai Wah Wu, Oct 18 2024
CROSSREFS
Cf. A000142, A004151, A008904 (mod 10).
Sequence in context: A243657 A321475 A356757 * A076126 A263692 A363962
KEYWORD
nonn,base,changed
STATUS
approved