login
Octuple factorial, 8-factorial, n!8, n!!!!!!!!.
15

%I #22 Sep 08 2022 08:45:23

%S 1,1,2,3,4,5,6,7,8,9,20,33,48,65,84,105,128,153,360,627,960,1365,1848,

%T 2415,3072,3825,9360,16929,26880,39585,55440,74865,98304,126225,

%U 318240,592515,967680,1464645,2106720,2919735,3932160,5175225,13366080

%N Octuple factorial, 8-factorial, n!8, n!!!!!!!!.

%H Harvey P. Dale, <a href="/A114800/b114800.txt">Table of n, a(n) for n = 0..1000</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, else a(n) = n*a(n-8).

%F Sum_{n>=0} 1/a(n) = A288095. - _Amiram Eldar_, Nov 10 2020

%e a(10) = 10 * a(10-8) = 10 * a(2) = 10 * 2 = 20.

%e a(20) = 20 * a(20-8) = 20 * a(12) = 20 * (12*a(12-8)) = 20 * 12 * a(4) = 20 * 12 * 4 = 960.

%e 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 := proc(n)

%p option remember;

%p if n < 1 then

%p 1;

%p else

%p n*procname(n-8) ;

%p end if;

%p end proc:

%p seq(A114800(n),n=0..40) ; # _R. J. Mathar_, Jun 23 2014

%t Table[Times@@Range[n,1,-8],{n,0,50}] (* _Harvey P. Dale_, Feb 17 2018 *)

%o (PARI) a(n)=if(n<1, 1, n*a(n-8));

%o vector(50, n, n--; a(n) ) \\ _G. C. Greubel_, Aug 21 2019

%o (Magma) b:=func< n | n le 8 select n else n*Self(n-8) >;

%o [1] cat [b(n): n in [1..50]]; // _G. C. Greubel_, Aug 21 2019

%o (Sage)

%o def a(n):

%o if (n<1): return 1

%o else: return n*a(n-8)

%o [a(n) for n in (0..50)] # _G. C. Greubel_, Aug 21 2019

%o (GAP)

%o a:= function(n)

%o if n<1 then return 1;

%o else return n*a(n-8);

%o fi;

%o end;

%o List([0..50], n-> a(n) ); # _G. C. Greubel_, Aug 21 2019

%Y Cf. A000142, A006882, A007661, A007662, A085157, A085158, A288095.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Feb 18 2006