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} 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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 18 2006
STATUS
approved