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A114796 Cumulative product of sextuple factorial A085158.

%I A114796 #13 Feb 16 2025 08:33:00
%S A114796 1,1,2,6,24,120,720,5040,80640,2177280,87091200,4790016000,
%T A114796 344881152000,31384184832000,7030057402368000,2847173247959040000,
%U A114796 1822190878693785600000,1703748471578689536000000
%N A114796 Cumulative product of sextuple factorial A085158.
%H A114796 G. C. Greubel, <a href="/A114796/b114796.txt">Table of n, a(n) for n = 0..91</a>
%H A114796 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>.
%F A114796 a(n) = Product_{j=0..n} j!!!!!!.
%F A114796 a(n) = Product_{j=0..n} j!6.
%F A114796 a(n) = Product_{j=0..n} A085158(j).
%F A114796 a(n) = n!!!!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2.
%F A114796 a(n) = n*(n-6)!!!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.
%e A114796 a(10) = 1!6 * 2!6 * 3!6 * 4!6 * 5!6 * 6!6 * 7!6 * 8!6 * 9!6 * 10!6
%e A114796 = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 16 * 27 * 40 = 87091200 = 2^11 * 3^5 * 5^2 * 7.
%e A114796 Note that a(10) + 1 = 87091201 is prime, as is a(9) + 1 = 2177281.
%p A114796 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
%t A114796 b[n_]:= b[n]= If[n<1, 1, n*b[n-6]]; a[n_]:= Product[b[j], {j,0,n}];
%t A114796 Table[a[n], {n, 0, 20}] (* _G. C. Greubel_, Aug 22 2019 *)
%o A114796 (PARI) b(n)=if(n<1, 1, n*b(n-6));
%o A114796 vector(20, n, n--; prod(j=0,n, b(j)) ) \\ _G. C. Greubel_, Aug 22 2019
%o A114796 (Magma) b:=func< n | n le 6 select n else n*Self(n-6) >;
%o A114796 [1] cat [(&*[b(j): j in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Aug 22 2019
%o A114796 (Sage)
%o A114796 def b(n):
%o A114796     if (n<1): return 1
%o A114796     else: return n*b(n-6)
%o A114796 [product(b(j) for j in (0..n)) for n in (0..20)] # _G. C. Greubel_, Aug 22 2019
%o A114796 (GAP)
%o A114796 b:= function(n)
%o A114796     if n<1 then return 1;
%o A114796     else return n*b(n-6);
%o A114796     fi;
%o A114796   end;
%o A114796 List([0..20], n-> Product([0..n], j-> b(j)) ); # _G. C. Greubel_, Aug 22 2019
%Y A114796 Cf. A000178, A006882, A007662, A085150, A085157, A085158, A114347.
%K A114796 easy,nonn
%O A114796 0,3
%A A114796 _Jonathan Vos Post_, Feb 18 2006