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A276267 a(n) = ( a(n-1)^2*a(n-2)^2*a(n-3)^2 + 1 ) / a(n-4), with a(0)=a(1)=a(2)=a(3)=1.

%I A276267 #18 Nov 18 2021 15:06:26
%S A276267 1,1,1,1,2,5,101,1020101,132690278976255013,
%T A276267 37379828474243017116309068570169440106423243719554
%N A276267 a(n) = ( a(n-1)^2*a(n-2)^2*a(n-3)^2 + 1 ) / a(n-4), with a(0)=a(1)=a(2)=a(3)=1.
%H A276267 Seiichi Manyama, <a href="/A276267/b276267.txt">Table of n, a(n) for n = 0..11</a>
%t A276267 RecurrenceTable[{a[n] == (a[n - 1]^2 a[n - 2]^2 a[n - 3]^2 + 1)/a[n - 4], a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 10}] (* _Michael De Vlieger_, Aug 26 2016 *)
%t A276267 nxt[{a_,b_,c_,d_}]:={b,c,d,(b^2 c^2 d^2+1)/a}; NestList[nxt,{1,1,1,1},10][[All,1]] (* _Harvey P. Dale_, Nov 18 2021 *)
%o A276267 (Ruby)
%o A276267 def A(m, n)
%o A276267   a = Array.new(m, 1)
%o A276267   ary = [1]
%o A276267   while ary.size < n + 1
%o A276267     i = (a[1..-1].inject(:*)) ** 2 + 1
%o A276267     break if i % a[0] > 0
%o A276267     a = *a[1..-1], i / a[0]
%o A276267     ary << a[0]
%o A276267   end
%o A276267   ary
%o A276267 end
%o A276267 def A276267(n)
%o A276267   A(4, n)
%o A276267 end
%Y A276267 Cf. A001519, A208209.
%K A276267 nonn
%O A276267 0,5
%A A276267 _Seiichi Manyama_, Aug 26 2016