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A007704 a(n+2) = (a(n) - 1)*a(n+1) + 1.

%I A007704 M0594 #36 Mar 19 2024 03:20:05
%S A007704 2,3,4,9,28,225,6076,1361025,8268226876,11253255215681025,
%T A007704 93044467205527772332546876,
%U A007704 1047053135870867396062743192203958743681025
%N A007704 a(n+2) = (a(n) - 1)*a(n+1) + 1.
%D A007704 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007704 Amiram Eldar, <a href="/A007704/b007704.txt">Table of n, a(n) for n = 1..18</a>
%H A007704 J. L. Davison and Jeffrey O. Shallit, <a href="https://doi.org/10.1007/BF01332350">Continued Fractions for Some Alternating Series</a>, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN362162050_0111&amp;DMDID=DMDLOG_0013&amp;LOGID=LOG_0013&amp;PHYSID=PHYS_0126">alternative link</a>.
%F A007704 a(n) = A006277(n) + 1. - _R. J. Mathar_, Apr 27 2007
%F A007704 Product_{k=1..n} a(k) = A006277(k)*A006277(k+1). - _Amiram Eldar_, Mar 19 2024
%p A007704 A007704 := proc(n) options remember; if n <= 2 then RETURN(n+1) else (A007704(n-2)-1)*A007704(n-1)+1; fi; end;
%t A007704 RecurrenceTable[{a[n] == a[n-1] (a[n-2] - 1) + 1, a[1] == 2, a[2] == 3}, a, {n, 1, 12}] (* _Jean-François Alcover_, Apr 05 2020 *)
%Y A007704 Cf. A006277.
%K A007704 nonn,easy
%O A007704 1,1
%A A007704 _N. J. A. Sloane_, _Jeffrey Shallit_