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A000304 a(n) = a(n-1)*a(n-2).

%I A000304 #56 Jan 05 2025 19:51:31
%S A000304 2,3,6,18,108,1944,209952,408146688,85691213438976,
%T A000304 34974584955819144511488,2997014624388697307377363936018956288,
%U A000304 104819342594514896999066634490728502944926883876041385836544
%N A000304 a(n) = a(n-1)*a(n-2).
%C A000304 A038500(a(n)) = A010098(n-2); for n > 2: A006519(a(n)) = A000301(n-3); A001222(a(n)) = A000045(n-1). - _Reinhard Zumkeller_, Jul 06 2014
%H A000304 T. D. Noe, <a href="/A000304/b000304.txt">Table of n, a(n) for n = 2..18</a>
%H A000304 Peter G. Anderson, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/55-5/Anderson.pdf">Notes & Extensions for a Remarkable Continued Fraction</a>, Fibonacci Quart. 55 (2017), no. 5, 9-14. Mentions this sequence.
%H A000304 Sergio Falcon, <a href="http://dx.doi.org/10.1080/0020739031000158362">Fibonacci's multiplicative sequence</a>, Int. J. Math. Edu. Sci. Technol. 34-2 (2003), 310-315. [_Sergio Falcon_, Nov 23 2009]
%F A000304 For n>=4, a(n) = 2^A000045(n-3)*3^A000045(n-2). - _Benoit Cloitre_, Sep 26 2003
%F A000304 For n > 2: a(n) = A000301(n-3) * A010098(n-2). - _Reinhard Zumkeller_, Jul 06 2014
%p A000304 A000304 := proc(n) option remember; if n <=3 then n else A000304(n-1)*A000304(n-2); fi; end;
%t A000304 nxt[{a_,b_}]:={b,a*b}; Transpose[NestList[nxt,{2,3},12]][[1]] (* _Harvey P. Dale_, Nov 16 2014 *)
%o A000304 (Haskell)
%o A000304 a000304 n = a000304_list !! (n-2)
%o A000304 a000304_list = 2 : 3 : zipWith (*) a000304_list (tail a000304_list)
%o A000304 -- _Reinhard Zumkeller_, Jul 06 2014
%Y A000304 Cf. A000045, A000301, A001222, A006519, A010098, A038500, A249406.
%K A000304 nonn
%O A000304 2,1
%A A000304 _N. J. A. Sloane_
%E A000304 More terms from _Vladimir Joseph Stephan Orlovsky_, Feb 17 2010