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A123144 a(1) = 1, a(n) = a(n-1) if n = 1 (mod 3), otherwise n*a(n-1).

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