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

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 33, 48, 65, 84, 105, 128, 153, 360, 627, 960, 1365, 1848, 2415, 3072, 3825, 9360, 16929, 26880, 39585, 55440, 74865, 98304, 126225, 318240, 592515, 967680, 1464645, 2106720, 2919735, 3932160, 5175225, 13366080

Offset: 0

Author

Jonathan Vos Post, Feb 18 2006

Keywords

• easy
• nonn

Examples

			a(10) = 10 * a(10-8) = 10 * a(2) = 10 * 2 = 20.
a(20) = 20 * a(20-8) = 20 * a(12) = 20 * (12*a(12-8)) = 20 * 12 * a(4) = 20 * 12 * 4 = 960.
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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Multifactorial.

Crossrefs

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

Programs

GAP

a:= function(n)
    if n<1 then return 1;
    else return n*a(n-8);
    fi;
  end;
List([0..50], n-> a(n) ); # G. C. Greubel, Aug 21 2019

Magma

b:=func< n | n le 8 select n else n*Self(n-8) >;
[1] cat [b(n): n in [1..50]]; // G. C. Greubel, Aug 21 2019

Maple

A114800 := proc(n)
    option remember;
    if n < 1 then
        1;
    else
        n*procname(n-8) ;
    end if;
end proc:
seq(A114800(n),n=0..40) ; # R. J. Mathar, Jun 23 2014

Mathematica

Table[Times@@Range[n,1,-8],{n,0,50}] (* Harvey P. Dale, Feb 17 2018 *)

PARI

a(n)=if(n<1, 1, n*a(n-8));
vector(50, n, n--; a(n) ) \\ G. C. Greubel, Aug 21 2019

Sage

def a(n):
    if (n<1): return 1
    else: return n*a(n-8)
[a(n) for n in (0..50)] # G. C. Greubel, Aug 21 2019

Formula

a(n) = 1 for n<1, else a(n) = n*a(n-8).

Sum_{n>=0} 1/a(n) = A288095. - Amiram Eldar, Nov 10 2020