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%I #18 Jul 16 2023 16:57:35
%S 1,2,6,6,30,180,180,1440,12960,12960,142560,1710720,1710720,23950080,
%T 359251200,359251200,6107270400,109930867200,109930867200,
%U 2198617344000,46170964224000,46170964224000,1061932177152000,25486372251648000,25486372251648000
%N a(1) = 1, a(n) = a(n-1) if n = 1 (mod 3), otherwise n*a(n-1).
%C Without duplicates this sequence is A293653.
%H Harvey P. Dale, <a href="/A123144/b123144.txt">Table of n, a(n) for n = 1..632</a>
%p a:= proc(n) option remember; `if`(n=0, 1,
%p `if`(irem(n, 3)=1, 1, n)*a(n-1))
%p end:
%p seq(a(n), n=1..32); # _Alois P. Heinz_, Jul 16 2023
%t a[n_]:= a[n]= If[n==1, 1, If[Mod[n,3]==1, a[n-1], n*a[n-1]]];
%t Table[a[n], {n,30}]
%t nxt[{n_,a_}]:={n+1,If[Mod[n+1,3]==1,a,a(n+1)]}; Transpose[NestList[nxt,{1,1},20]][[2]] (* _Harvey P. Dale_, Jul 22 2014 *)
%o (Magma)
%o function a(n)
%o if n eq 1 then return 1;
%o elif (n mod 3) eq 1 then return a(n-1);
%o else return n*a(n-1);
%o end if;
%o end function;
%o [a(n): n in [1..40]]; // _G. C. Greubel_, Jul 16 2023
%o (SageMath)
%o def a(n): # A123144
%o if (n==1): return 1
%o elif (n%3==1): return a(n-1)
%o else: return n*a(n-1)
%o [a(n) for n in range(1,41)] # _G. C. Greubel_, Jul 16 2023
%Y Cf. A007559, A123145, A293653.
%K nonn
%O 1,2
%A _Roger L. Bagula_, Oct 01 2006
%E Edited by _N. J. A. Sloane_, Oct 04 2006
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