The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #11 Mar 23 2017 14:42:34
%S 2,8,44,704,124784,3114359072,1616538741858202448,
%T 373313929132642872042128187516973184,
%U 17420411210556488056172048238850552742971470265342499948186222078482064
%N a(1) = 2, a(n+1) = a(n) * (1 + n + a(n))/n.
%C The next term has 139 digits.
%H StackExchange - Mathematics, <a href="http://math.stackexchange.com/questions/178614/quadratic-recurrence-relation">Quadratic Recurrence Relation</a> (sequence b(n) in the reference).
%F a(n) ~ n * c^(2^n), where c = 1.36534926036757464312824443040683531215776134381623126072...
%t FoldList[#1*(1+#2+#1)/#2&,2,Range@8] (* _Ivan N. Ianakiev_, Jun 06 2015 *)
%o (Maxima) a(n) := if n = 1 then 2 else a(n-1)*(n+a(n-1))/(n-1) $
%o makelist(a(n),n,1,12); _Emanuele Munarini_, Mar 23 2017
%K nonn
%O 1,1
%A _Vaclav Kotesovec_, Jun 06 2015