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A276416 a(n) = a(n-1)*(1 + a(n-1)/a(n-4)), with a(0) = a(1) = a(2) = a(3) = 1.

%I A276416 #19 May 08 2025 10:35:43
%S A276416 1,1,1,1,2,6,42,1806,1632624,444245153520,4698898962968253924720,
%T A276416 12225720633546031105793020748137513851120,
%U A276416 91550929674875028299231929179221527919681972461210779957660001348767546720
%N A276416 a(n) = a(n-1)*(1 + a(n-1)/a(n-4)), with a(0) = a(1) = a(2) = a(3) = 1.
%H A276416 Seiichi Manyama, <a href="/A276416/b276416.txt">Table of n, a(n) for n = 0..16</a>
%F A276416 0 = a(n)*(a(n+3) - a(n+4)) + a(n+3)*a(n+3) for all n>=0.
%F A276416 A133400(n) = a(n+1)/a(n).
%t A276416 RecurrenceTable[{a[n] == a[n - 1] (1 + a[n - 1]/a[n - 4]), a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 12}] (* _Michael De Vlieger_, Sep 04 2016 *)
%t A276416 nxt[{a_,b_,c_,d_}]:={b,c,d,d(1+d/a)}; NestList[nxt,{1,1,1,1},12][[;;,1]] (* _Harvey P. Dale_, May 08 2025 *)
%o A276416 (Ruby)
%o A276416 def A(m, n)
%o A276416   a = Array.new(m, 1)
%o A276416   ary = [1]
%o A276416   while ary.size < n + 1
%o A276416     break if a[-1] % a[0] > 0
%o A276416     a = *a[1..-1], a[-1] * (1 + a[-1] / a[0])
%o A276416     ary << a[0]
%o A276416   end
%o A276416   ary
%o A276416 end
%o A276416 def A276416(n)
%o A276416   A(4, n)
%o A276416 end
%Y A276416 Cf. A133400, A250309.
%K A276416 nonn
%O A276416 0,5
%A A276416 _Seiichi Manyama_, Sep 02 2016