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A114800 Octuple factorial, 8-factorial, n!8, n!!!!!!!!.

%I A114800 #23 Feb 16 2025 08:33:00
%S A114800 1,1,2,3,4,5,6,7,8,9,20,33,48,65,84,105,128,153,360,627,960,1365,1848,
%T A114800 2415,3072,3825,9360,16929,26880,39585,55440,74865,98304,126225,
%U A114800 318240,592515,967680,1464645,2106720,2919735,3932160,5175225,13366080
%N A114800 Octuple factorial, 8-factorial, n!8, n!!!!!!!!.
%H A114800 Harvey P. Dale, <a href="/A114800/b114800.txt">Table of n, a(n) for n = 0..1000</a>
%H A114800 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>.
%F A114800 a(n) = 1 for n<1, else a(n) = n*a(n-8).
%F A114800 Sum_{n>=0} 1/a(n) = A288095. - _Amiram Eldar_, Nov 10 2020
%e A114800 a(10) = 10 * a(10-8) = 10 * a(2) = 10 * 2 = 20.
%e A114800 a(20) = 20 * a(20-8) = 20 * a(12) = 20 * (12*a(12-8)) = 20 * 12 * a(4) = 20 * 12 * 4 = 960.
%e A114800 a(30) = 30 * a(30-8) = 30 * a(22) = 30 * (22*a(22-8)) = 30 * 22 * a(14) = 30 * 22 * (14*a(14-8)) = 30 * 22 * 14 * 6 = 55440.
%p A114800 A114800 := proc(n)
%p A114800     option remember;
%p A114800     if n < 1 then
%p A114800         1;
%p A114800     else
%p A114800         n*procname(n-8) ;
%p A114800     end if;
%p A114800 end proc:
%p A114800 seq(A114800(n),n=0..40) ; # _R. J. Mathar_, Jun 23 2014
%t A114800 Table[Times@@Range[n,1,-8],{n,0,50}] (* _Harvey P. Dale_, Feb 17 2018 *)
%o A114800 (PARI) a(n)=if(n<1, 1, n*a(n-8));
%o A114800 vector(50, n, n--; a(n) ) \\ _G. C. Greubel_, Aug 21 2019
%o A114800 (Magma) b:=func< n | n le 8 select n else n*Self(n-8) >;
%o A114800 [1] cat [b(n): n in [1..50]]; // _G. C. Greubel_, Aug 21 2019
%o A114800 (Sage)
%o A114800 def a(n):
%o A114800     if (n<1): return 1
%o A114800     else: return n*a(n-8)
%o A114800 [a(n) for n in (0..50)] # _G. C. Greubel_, Aug 21 2019
%o A114800 (GAP)
%o A114800 a:= function(n)
%o A114800     if n<1 then return 1;
%o A114800     else return n*a(n-8);
%o A114800     fi;
%o A114800   end;
%o A114800 List([0..50], n-> a(n) ); # _G. C. Greubel_, Aug 21 2019
%Y A114800 Cf. A000142, A006882, A007661, A007662, A085157, A085158, A288095.
%K A114800 easy,nonn
%O A114800 0,3
%A A114800 _Jonathan Vos Post_, Feb 18 2006