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%I #31 Sep 08 2022 08:45:11
%S 1,1,2,3,4,5,6,14,24,36,50,66,168,312,504,750,1056,2856,5616,9576,
%T 15000,22176,62832,129168,229824,375000,576576,1696464,3616704,
%U 6664896,11250000,17873856,54286848,119351232,226606464,393750000,643458816
%N Quintuple factorials, 5-factorials, n!!!!!, n!5.
%C 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.
%H G. C. Greubel, <a href="/A085157/b085157.txt">Table of n, a(n) for n = 0..1000</a>
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/Multifactorials">Multifactorials</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>.
%F a(n) = 1 for n < 1, otherwise a(n) = n*a(n-5).
%F Sum_{n>=0} 1/a(n) = A288092. - _Amiram Eldar_, Nov 10 2020
%e a(12) = 168 because 12*a(12-5) = 12*a(7) = 12*14 = 168.
%p a:= n-> `if`(n < 1, 1, n*a(n-5)) end proc; seq(a(n), n = 0..40); # _G. C. Greubel_, Aug 18 2019
%t a[n_]:= If[n<1, 1, n*a[n-5]]; Table[a[n], {n,0,40}] (* _G. C. Greubel_, Aug 18 2019 *)
%t Table[Times@@Range[n,1,-5],{n,0,40}] (* _Harvey P. Dale_, May 12 2020 *)
%o (PARI) a(n)=if(n<1, 1, n*a(n-5))
%o for(n=0,50,print1(a(n),",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 19 2006
%o (Magma)
%o b:= func< n | (n lt 6) select n else n*Self(n-5) >;
%o [1] cat [b(n): n in [1..40]]; // _G. C. Greubel_, Aug 18 2019
%o (Sage)
%o def a(n):
%o if (n<1): return 1
%o else: return n*a(n-5)
%o [a(n) for n in (0..40)] # _G. C. Greubel_, Aug 18 2019
%o (GAP)
%o a:= function(n)
%o if n<1 then return 1;
%o else return n*a(n-5);
%o fi;
%o end;
%o List([0..40], n-> a(n) ); # _G. C. Greubel_, Aug 18 2019
%o (Python)
%o def A085157(n):
%o if n <= 0:
%o return 1
%o else:
%o return n*A085157(n-5)
%o n = 0
%o while n <= 40:
%o print(n,A085157(n))
%o n = n+1 # _A.H.M. Smeets_, Aug 18 2019
%Y Cf. n!:A000142, n!!:A006882, n!!!:A007661, n!!!!:A007662, n!!!!!!:A085158, 5-factorial primes: n!!!!!+1:A085148, n!!!!!-1:A085149.
%Y Cf. A288092.
%K nonn
%O 0,3
%A _Hugo Pfoertner_, Jun 21 2003
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