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A356858 a(n) is the product of the first n numbers not divisible by 5.

%I A356858 #17 Nov 03 2024 16:13:42
%S A356858 1,1,2,6,24,144,1008,8064,72576,798336,9580032,124540416,1743565824,
%T A356858 27897053184,474249904128,8536498274304,162193467211776,
%U A356858 3406062811447296,74933381851840512,1723467782592331776,41363226782215962624,1075443896337615028224,29036985201115605762048
%N A356858 a(n) is the product of the first n numbers not divisible by 5.
%C A356858 Unlike the factorial number n!, a(n) does not have trailing zeros.
%H A356858 Harvey P. Dale, <a href="/A356858/b356858.txt">Table of n, a(n) for n = 0..434</a>
%F A356858 a(n) = Product_{k=1..n} A047201(k).
%F A356858 a(n) = A047201(n)!/(floor(A047201(n)/5)!*5^floor(A047201(n)/5)) for n > 0.
%t A356858 Table[Product[Floor[(5k-1)/4], {k,n}], {n,0,22}] (* or *)
%t A356858 Join[{1}, Table[Floor[(5n-1)/4]!/(Floor[Floor[(5n-1)/4]/5]!*5^Floor[Floor[(5n-1)/4]/5]), {n,22}]]
%t A356858 Join[{1},FoldList[Times,Table[If[Mod[n,5]==0,Nothing,n],{n,30}]]] (* _Harvey P. Dale_, Nov 03 2024 *)
%o A356858 (Python)
%o A356858 from math import prod
%o A356858 def a(n): return prod((5*k-1)//4 for k in range(1, n+1))
%o A356858 print([a(n) for n in range(23)]) # _Michael S. Branicky_, Sep 01 2022
%Y A356858 Cf. A000142, A000351, A002266, A047201.
%Y A356858 Cf. A356859 (number of zero digits), A356860 (number of digits), A356861 (number of nonzero digits).
%K A356858 nonn
%O A356858 0,3
%A A356858 _Stefano Spezia_, Sep 01 2022