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A085157
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Quintuple factorials, 5-factorials, n!!!!!, n!5.
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24
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1, 1, 2, 3, 4, 5, 6, 14, 24, 36, 50, 66, 168, 312, 504, 750, 1056, 2856, 5616, 9576, 15000, 22176, 62832, 129168, 229824, 375000, 576576, 1696464, 3616704, 6664896, 11250000, 17873856, 54286848, 119351232, 226606464, 393750000, 643458816
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OFFSET
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0,3
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COMMENTS
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The term "Quintuple factorial numbers" is also used for the sequences A008546, A008548, A052562, A047055, A047056 which have a different definition. The definition given here is the one commonly used.
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LINKS
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FORMULA
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a(n) = 1 for n < 1, otherwise a(n) = n*a(n-5).
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EXAMPLE
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a(12) = 168 because 12*a(12-5) = 12*a(7) = 12*14 = 168.
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MAPLE
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a:= n-> `if`(n < 1, 1, n*a(n-5)) end proc; seq(a(n), n = 0..40); # G. C. Greubel, Aug 18 2019
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MATHEMATICA
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a[n_]:= If[n<1, 1, n*a[n-5]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Aug 18 2019 *)
Table[Times@@Range[n, 1, -5], {n, 0, 40}] (* Harvey P. Dale, May 12 2020 *)
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PROG
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(PARI) a(n)=if(n<1, 1, n*a(n-5))
for(n=0, 50, print1(a(n), ", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006
(Magma)
b:= func< n | (n lt 6) select n else n*Self(n-5) >;
(Sage)
def a(n):
if (n<1): return 1
else: return n*a(n-5)
(GAP)
a:= function(n)
if n<1 then return 1;
else return n*a(n-5);
fi;
end;
(Python)
if n <= 0:
return 1
else:
n = 0
while n <= 40:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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