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%I #20 Sep 08 2022 08:45:11
%S 1,1,2,3,4,5,6,7,16,27,40,55,72,91,224,405,640,935,1296,1729,4480,
%T 8505,14080,21505,31104,43225,116480,229635,394240,623645,933120,
%U 1339975,3727360,7577955,13404160,21827575,33592320,49579075,141639680
%N Sextuple factorials, 6-factorials, n!!!!!!, n!6.
%C The term "Sextuple factorial numbers" is also used for the sequences A008542, A008543, A011781, A047058, A047657, A049308, which have a different definition. The definition given here is the one commonly used.
%H G. C. Greubel, <a href="/A085158/b085158.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>.
%F a(n)=1 for n < 1, otherwise a(n) = n*a(n-6).
%F Sum_{n>=0} 1/a(n) = A288093. - _Amiram Eldar_, Nov 10 2020
%e a(14) = 224 because 14*a(14-6) = 14*a(8) = 14*16 = 224.
%p a:= n-> `if`(n<1, 1, n*a(n-6)); seq(a(n), n=0..40); # _G. C. Greubel_, Aug 21 2019
%t Table[Times@@Range[n,1,-6],{n,0,40}] (* _Harvey P. Dale_, Aug 10 2019 *)
%o (PARI) a(n)=if(n<1, 1, n*a(n-6));
%o vector(40, n, n--; a(n) ) \\ _G. C. Greubel_, Aug 21 2019
%o (Magma) b:=func< n | n le 6 select n else n*Self(n-6) >;
%o [1] cat [b(n): n in [1..40]]; // _G. C. Greubel_, Aug 21 2019
%o (Sage)
%o def a(n):
%o if (n<1): return 1
%o else: return n*a(n-6)
%o [a(n) for n in (0..40)] # _G. C. Greubel_, Aug 21 2019
%o (GAP)
%o a:= function(n)
%o if n<1 then return 1;
%o else return n*a(n-6);
%o fi;
%o end;
%o List([0..40], n-> a(n) ); # _G. C. Greubel_, Aug 21 2019
%Y Cf. n!:A000142, n!!:A006882, n!!!:A007661, n!!!!:A007662, n!!!!!:A085157, 6-factorial primes: n!!!!!!+1:A085150, n!!!!!!-1:A051592.
%Y Cf. A288093.
%K nonn
%O 0,3
%A _Hugo Pfoertner_, Jun 21 2003
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