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A141609 a(n) = (a(n-1)*a(n-2) + a(n-1)^2)/a(n-3), with a(1) = a(2) = a(3) = 1.

%I A141609 #21 Sep 22 2024 11:05:33
%S A141609 1,1,1,2,6,48,1296,290304,1763596800,2400297571123200,
%T A141609 19846204885558066176000000,
%U A141609 223334408639880528216369404299444224000000,20780031060559302184531906881808103844643569442380668928000000000000
%N A141609 a(n) = (a(n-1)*a(n-2) + a(n-1)^2)/a(n-3), with a(1) = a(2) = a(3) = 1.
%H A141609 G. C. Greubel, <a href="/A141609/b141609.txt">Table of n, a(n) for n = 1..18</a>
%F A141609 a(n+1) / a(n) = A006277(n-1). - _Michael Somos_, Dec 29 2012
%t A141609 a[n_]:= a[n]= If[n<4,1,(a[n-1]*a[n-2] +a[n-1]^2)/a[n-3]]; Table[a[n], {n,15}]
%t A141609 RecurrenceTable[{a[1]==a[2]==a[3]==1,a[n]==(a[n-1]a[n-2]+a[n-1]^2)/a[n-3]}, a,{n,14}] (* _Harvey P. Dale_, Oct 01 2017 *)
%o A141609 (Magma) [n le 3 select 1 else (Self(n-1)*Self(n-2) +Self(n-1)^2)/Self(n-3): n in [1..15]]; // _G. C. Greubel_, Sep 21 2024
%o A141609 (SageMath)
%o A141609 def a(n): # a = A141609
%o A141609     if n<3: return 1
%o A141609     else: return (a(n-1)*a(n-2) +a(n-1)^2)/a(n-3)
%o A141609 [a(n) for n in range(1,16)] # _G. C. Greubel_, Sep 21 2024
%Y A141609 Cf. A006277, A006720.
%K A141609 nonn
%O A141609 1,4
%A A141609 _Roger L. Bagula_, Aug 22 2008
%E A141609 Edited by _N. J. A. Sloane_, Aug 24 2008