A114790 Cumulative product of quintuple factorial A085157.

1, 1, 2, 6, 24, 120, 720, 10080, 241920, 8709120, 435456000, 28740096000, 4828336128000, 1506440871936000, 759246199455744000, 569434649591808000000, 601322989968949248000000

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..84

Eric Weisstein's World of Mathematics, Multifactorial.

Formula

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

a(n) = Product_{[j=0..n} j!5.

a(n) = Product_{j=0..n} A085157(j).

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

a(n) = n*(n-5)!!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.

Example

a(10) = 1!!!!! * 2!!!!! * 3!!!!! * 4!!!!! * 5!!!!! * 6!!!!! * 7!!!!! * 8!!!!! * 9!!!!! * 10!!!!! = 1 * 2 * 3 * 4 * 5 * 6 * 14 * 24 * 36 * 50 = 435456000 = 2^11 * 3^5 * 5^3 * 7.

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 21 2019

Mathematica

b[n_]:= If[n<1, 1, n*b[n-5]]; a[n_]:= Product[b[j], {j, 0, n}]; Table[a[n], {n, 0, 20}] (* G. C. Greubel, Aug 21 2019 *)

Prog

(PARI) b(n)=if(n<1, 1, n*b(n-5));
vector(20, n, n--; prod(j=0, n, b(j)) ) \\ G. C. Greubel, Aug 21 2019
(Magma) b:= func< n | n eq 0 select 1 else (n lt 6) select n else n*Self(n-5) >;
[(&*[b(j): j in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 21 2019
(Sage)
@CachedFunction
def b(n):
    if (n<1): return 1
    else: return n*b(n-5)
[product(b(j) for j in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 21 2019
(GAP)
b:= function(n)
    if n<1 then return 1;
    else return n*b(n-5);
    fi;
  end;
List([0..20], n-> Product([0..n], j-> b(j)) ); # G. C. Greubel, Aug 21 2019

Crossrefs

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

Sequence in context: A129655 A114796 A265086 * A352430 A292749 A351984

Adjacent sequences: A114787 A114788 A114789 * A114791 A114792 A114793

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 18 2006

Status

approved