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

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..91

Eric Weisstein's World of Mathematics, Multifactorial.

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.

Example

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.

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 *)

Prog

(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
(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
(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
(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

Crossrefs

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

Sequence in context: A130641 A350113 A129655 * A265086 A114790 A352430

Adjacent sequences: A114793 A114794 A114795 * A114797 A114798 A114799

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 18 2006

Status

approved