A356858 - OEIS

%I #17 Nov 03 2024 16:13:42

%S 1,1,2,6,24,144,1008,8064,72576,798336,9580032,124540416,1743565824,

%T 27897053184,474249904128,8536498274304,162193467211776,

%U 3406062811447296,74933381851840512,1723467782592331776,41363226782215962624,1075443896337615028224,29036985201115605762048

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

%C Unlike the factorial number n!, a(n) does not have trailing zeros.

%H Harvey P. Dale, <a href="/A356858/b356858.txt">Table of n, a(n) for n = 0..434</a>

%F a(n) = Product_{k=1..n} A047201(k).

%F a(n) = A047201(n)!/(floor(A047201(n)/5)!*5^floor(A047201(n)/5)) for n > 0.

%t Table[Product[Floor[(5k-1)/4], {k,n}], {n,0,22}] (* or *)

%t Join[{1}, Table[Floor[(5n-1)/4]!/(Floor[Floor[(5n-1)/4]/5]!*5^Floor[Floor[(5n-1)/4]/5]), {n,22}]]

%t Join[{1},FoldList[Times,Table[If[Mod[n,5]==0,Nothing,n],{n,30}]]] (* _Harvey P. Dale_, Nov 03 2024 *)

%o (Python)

%o from math import prod

%o def a(n): return prod((5*k-1)//4 for k in range(1, n+1))

%o print([a(n) for n in range(23)]) # _Michael S. Branicky_, Sep 01 2022

%Y Cf. A000142, A000351, A002266, A047201.

%Y Cf. A356859 (number of zero digits), A356860 (number of digits), A356861 (number of nonzero digits).

%K nonn

%O 0,3

%A _Stefano Spezia_, Sep 01 2022