Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M0594 #36 Mar 19 2024 03:20:05
%S 2,3,4,9,28,225,6076,1361025,8268226876,11253255215681025,
%T 93044467205527772332546876,
%U 1047053135870867396062743192203958743681025
%N a(n+2) = (a(n) - 1)*a(n+1) + 1.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Amiram Eldar, <a href="/A007704/b007704.txt">Table of n, a(n) for n = 1..18</a>
%H 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&DMDID=DMDLOG_0013&LOGID=LOG_0013&PHYSID=PHYS_0126">alternative link</a>.
%F a(n) = A006277(n) + 1. - _R. J. Mathar_, Apr 27 2007
%F Product_{k=1..n} a(k) = A006277(k)*A006277(k+1). - _Amiram Eldar_, Mar 19 2024
%p A007704 := proc(n) options remember; if n <= 2 then RETURN(n+1) else (A007704(n-2)-1)*A007704(n-1)+1; fi; end;
%t 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 Cf. A006277.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, _Jeffrey Shallit_