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 A114790 Cumulative product of quintuple factorial A085157. 2
 1, 1, 2, 6, 24, 120, 720, 10080, 241920, 8709120, 435456000, 28740096000, 4828336128000, 1506440871936000, 759246199455744000, 569434649591808000000, 601322989968949248000000 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)