A114796 Cumulative product of sextuple factorial A085158.

1, 1, 2, 6, 24, 120, 720, 5040, 80640, 2177280, 87091200, 4790016000, 344881152000, 31384184832000, 7030057402368000, 2847173247959040000, 1822190878693785600000, 1703748471578689536000000

Offset: 0

Author

Jonathan Vos Post, Feb 18 2006

Keywords

• easy
• nonn

Examples

			a(10) = 1!6 * 2!6 * 3!6 * 4!6 * 5!6 * 6!6 * 7!6 * 8!6 * 9!6 * 10!6
= 1 * 2 * 3 * 4 * 5 * 6 * 7 * 16 * 27 * 40 = 87091200 = 2^11 * 3^5 * 5^2 * 7.
Note that a(10) + 1 = 87091201 is prime, as is a(9) + 1 = 2177281.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..91
• Eric Weisstein's World of Mathematics, Multifactorial.

Crossrefs

Cf. A000178, A006882, A007662, A085150, A085157, A085158, A114347.

Programs

GAP

b:= function(n)
    if n<1 then return 1;
    else return n*b(n-6);
    fi;
  end;
List([0..20], n-> Product([0..n], j-> b(j)) ); # G. C. Greubel, Aug 22 2019

Magma

b:=func< n | n le 6 select n else n*Self(n-6) >;
[1] cat [(&*[b(j): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 22 2019

Maple

b:= n-> `if`(n<1, 1, n*b(n-5)); a:= n-> product(b(j), j = 0..n); seq(a(n), n = 0..20); # G. C. Greubel, Aug 22 2019

Mathematica

b[n_]:= b[n]= If[n<1, 1, n*b[n-6]]; a[n_]:= Product[b[j], {j,0,n}];
Table[a[n], {n, 0, 20}] (* G. C. Greubel, Aug 22 2019 *)

PARI

b(n)=if(n<1, 1, n*b(n-6));
vector(20, n, n--; prod(j=0,n, b(j)) ) \\ G. C. Greubel, Aug 22 2019

Sage

def b(n):
    if (n<1): return 1
    else: return n*b(n-6)
[product(b(j) for j in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 22 2019

Formula

a(n) = Product_{j=0..n} j!!!!!!.

a(n) = Product_{j=0..n} j!6.

a(n) = Product_{j=0..n} A085158(j).

a(n) = n!!!!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2.

a(n) = n*(n-6)!!!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.