%I #10 Oct 01 2015 17:45:31
%S 1,1,2,4,8,24,112,944,22880,2564448,2420884672,55389846424256,
%T 142044380887832220032,343873064435082883562892998016,
%U 19047076228497528742755382412205052966716160
%N a(0) = a(1) = 1, a(2) = 2; a(n) = 2*a(n-2) + a(n-1)*a(n-3).
%C This is a recurrence relation which has 1,1 and 2 as the base cases and the n-th term is obtained by multiplying the (n-2)th term by 2 and adding it with the product of (n-1)th and (n-3)rd term.
%F a(n) ~ c^(d^n), where d = 1.465571231876768026... is the root of the equation d^3 = d^2 + 1 and c = 1.604048928929157460568... . - _Vaclav Kotesovec_, Oct 01 2015
%p f:=proc(n) option remember;
%p if n <= 1 then 1 elif n=2 then 2 else
%p f(n-1)*f(n-3)+2*f(n-2); fi; end;
%p [seq(f(n),n=0..15)]; # _N. J. A. Sloane_, Oct 01 2015
%t RecurrenceTable[{a[0]==a[1]==1,a[2]==2,a[n]==2a[n-2]+a[n-1]a[n-3]},a,{n,20}] (* _Harvey P. Dale_, Oct 01 2015 *)
%K easy,nonn
%O 0,3
%A Mohit Maheshwari (mohitmahe1989(AT)gmail.com), Jan 19 2008
%E Corrected by _Harvey P. Dale_, Oct 01 2015