A141609 - OEIS

%I #21 Sep 22 2024 11:05:33

%S 1,1,1,2,6,48,1296,290304,1763596800,2400297571123200,

%T 19846204885558066176000000,

%U 223334408639880528216369404299444224000000,20780031060559302184531906881808103844643569442380668928000000000000

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

%H G. C. Greubel, <a href="/A141609/b141609.txt">Table of n, a(n) for n = 1..18</a>

%F a(n+1) / a(n) = A006277(n-1). - _Michael Somos_, Dec 29 2012

%t 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 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 (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 (SageMath)

%o def a(n): # a = A141609

%o     if n<3: return 1

%o     else: return (a(n-1)*a(n-2) +a(n-1)^2)/a(n-3)

%o [a(n) for n in range(1,16)] # _G. C. Greubel_, Sep 21 2024

%Y Cf. A006277, A006720.

%K nonn

%O 1,4

%A _Roger L. Bagula_, Aug 22 2008

%E Edited by _N. J. A. Sloane_, Aug 24 2008