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A123145 a(1) = 1, a(n) = a(n-1) if n == 1 (mod 4), otherwise a(n) = n * a(n-1) for n >= 2.

%I A123145 #31 Jul 16 2023 16:56:53
%S A123145 1,2,6,24,24,144,1008,8064,8064,80640,887040,10644480,10644480,
%T A123145 149022720,2235340800,35765452800,35765452800,643778150400,
%U A123145 12231784857600,244635697152000,244635697152000,5381985337344000,123785662758912000,2970855906213888000
%N A123145 a(1) = 1, a(n) = a(n-1) if n == 1 (mod 4), otherwise a(n) = n * a(n-1) for n >= 2.
%C A123145 Terms which repeat appear to be denominators of g.f. 0F2(--; 1/2, 3/4; z^4/64), which begin 24, 8064, 10644480, 35765452800, ... - _Benedict W. J. Irwin_, Jun 15 2018
%H A123145 G. C. Greubel, <a href="/A123145/b123145.txt">Table of n, a(n) for n = 1..500</a>
%F A123145 Conjecture: E.g.f.: E(x)=d(G(0))/dx  where G(k) = 1 + x/(4*k+1 - x*(4*k+1)/(1 + x - x/(1 + x - x/(x + 1/G(k+1) )))), or shift on 1 left G(0); (continued fraction,5-step). - _Sergei N. Gladkovskii_, Nov 26 2012
%p A123145 a:= proc(n) option remember; `if`(n=0, 1,
%p A123145       `if`(irem(n, 4)=1, 1, n)*a(n-1))
%p A123145     end:
%p A123145 seq(a(n), n=1..24);  # _Alois P. Heinz_, Jul 16 2023
%t A123145 a[n_]:= a[n]= If[n==1, 1, If[Mod[n,4]==1, a[n-1], n*a[n-1]]];
%t A123145 Table[a[n], {n,30}]
%o A123145 (Magma)
%o A123145 function a(n) // a = A123145
%o A123145   if n eq 1 then return 1;
%o A123145   elif (n mod 4) eq 1 then return a(n-1);
%o A123145   else return n*a(n-1);
%o A123145   end if;
%o A123145 end function;
%o A123145 [a(n): n in [1..40]]; // _G. C. Greubel_, Jul 16 2023
%o A123145 (SageMath)
%o A123145 def a(n): # A123145
%o A123145     if (n==1): return 1
%o A123145     elif (n%4==1): return a(n-1)
%o A123145     else: return n*a(n-1)
%o A123145 [a(n) for n in range(1,41)] # _G. C. Greubel_, Jul 16 2023
%Y A123145 Cf. A007559, A007696.
%K A123145 nonn
%O A123145 1,2
%A A123145 _Roger L. Bagula_, Oct 01 2006
%E A123145 Edited by _N. J. A. Sloane_, Oct 04 2006
%E A123145 More terms from _Bruno Berselli_, Nov 27 2012