%I #17 Sep 04 2016 18:55:40
%S 1,1,1,1,2,6,42,1806,1632624,444245153520,4698898962968253924720,
%T 12225720633546031105793020748137513851120,
%U 91550929674875028299231929179221527919681972461210779957660001348767546720
%N a(n) = a(n-1)*(1 + a(n-1)/a(n-4)), with a(0) = a(1) = a(2) = a(3) = 1.
%H Seiichi Manyama, <a href="/A276416/b276416.txt">Table of n, a(n) for n = 0..16</a>
%F 0 = a(n)*(a(n+3) - a(n+4)) + a(n+3)*a(n+3) for all n>=0.
%F A133400(n) = a(n+1)/a(n).
%t 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 *)
%o (Ruby)
%o def A(m, n)
%o a = Array.new(m, 1)
%o ary = [1]
%o while ary.size < n + 1
%o break if a[-1] % a[0] > 0
%o a = *a[1..-1], a[-1] * (1 + a[-1] / a[0])
%o ary << a[0]
%o end
%o ary
%o end
%o def A276416(n)
%o A(4, n)
%o end
%Y Cf. A133400, A250309.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Sep 02 2016