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A288327 Decuple factorial, 10-factorial, n!10, n!!!!!!!!!!.

%I A288327 #24 Feb 16 2025 08:33:47
%S A288327 1,1,2,3,4,5,6,7,8,9,10,11,24,39,56,75,96,119,144,171,200,231,528,897,
%T A288327 1344,1875,2496,3213,4032,4959,6000,7161,16896,29601,45696,65625,
%U A288327 89856,118881,153216,193401,240000,293601,709632,1272843,2010624,2953125,4133376
%N A288327 Decuple factorial, 10-factorial, n!10, n!!!!!!!!!!.
%H A288327 Robert Price, <a href="/A288327/b288327.txt">Table of n, a(n) for n = 0..803</a>
%H A288327 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>.
%F A288327 a(n)=1 for n < 1, otherwise a(n) = n*a(n-10).
%F A288327 Sum_{n>=0} 1/a(n) = A342033. - _Amiram Eldar_, May 23 2022
%e A288327 a(13) = 13 * 3 * 1 = 39.
%p A288327 a:= n-> `if`(n<1, 1, n*a(n-10)); seq(a(n), n=0..50); # _G. C. Greubel_, Aug 22 2019
%t A288327 MultiFactorial[n_, k_]:=If[n<1, 1 ,n*MultiFactorial[n-k, k]];
%t A288327 Table[MultiFactorial[i, 10], {i, 0, 100}]
%t A288327 Table[Times@@Range[n,1,-10],{n,0,50}] (* _Harvey P. Dale_, Aug 11 2019 *)
%o A288327 (PARI) a(n)=if(n<1, 1, n*a(n-10));
%o A288327 vector(40, n, n--; a(n) ) \\ _G. C. Greubel_, Aug 22 2019
%o A288327 (Magma) b:=func< n | n le 10 select n else n*Self(n-10) >;
%o A288327 [1] cat [b(n): n in [1..50]]; // _G. C. Greubel_, Aug 22 2019
%o A288327 (Sage)
%o A288327 def a(n):
%o A288327     if (n<1): return 1
%o A288327     else: return n*a(n-10)
%o A288327 [a(n) for n in (0..50)] # _G. C. Greubel_, Aug 22 2019
%o A288327 (GAP)
%o A288327 a:= function(n)
%o A288327     if n<1 then return 1;
%o A288327     else return n*a(n-10);
%o A288327     fi;
%o A288327   end;
%o A288327 List([0..50], n-> a(n) ); # _G. C. Greubel_, Aug 22 2019
%Y A288327 Cf. A006852, A007661, A007662, A085157, A085158, A114799, A114800, A114806, A342033.
%K A288327 easy,nonn
%O A288327 0,3
%A A288327 _Robert Price_, Jun 07 2017