A085157 Quintuple factorials, 5-factorials, n!!!!!, n!5.
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
Offset: 0
Keywords
Examples
a(12) = 168 because 12*a(12-5) = 12*a(7) = 12*14 = 168.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Peter Luschny, Multifactorials
- Eric Weisstein's World of Mathematics, Multifactorial.
Crossrefs
Programs
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GAP
a:= function(n) if n<1 then return 1; else return n*a(n-5); fi; end; List([0..40], n-> a(n) ); # G. C. Greubel, Aug 18 2019 -
Magma
b:= func< n | (n lt 6) select n else n*Self(n-5) >; [1] cat [b(n): n in [1..40]]; // G. C. Greubel, Aug 18 2019
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Maple
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
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 *) -
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
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Python
def A085157(n): if n <= 0: return 1 else: return n*A085157(n-5) n = 0 while n <= 40: print(n,A085157(n)) n = n+1 # A.H.M. Smeets, Aug 18 2019
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Sage
def a(n): if (n<1): return 1 else: return n*a(n-5) [a(n) for n in (0..40)] # G. C. Greubel, Aug 18 2019
Formula
a(n) = 1 for n < 1, otherwise a(n) = n*a(n-5).
Sum_{n>=0} 1/a(n) = A288092. - Amiram Eldar, Nov 10 2020
Comments