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

Author

Jonathan Vos Post, Feb 18 2006

Keywords

• easy
• nonn

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..84
• Eric Weisstein's World of Mathematics, Multifactorial.

Crossrefs

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

Programs

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

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

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 *)

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

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

Formula

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.