This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001697 M1902 N0751 #63 Jan 09 2025 08:22:47
%S A001697 1,1,2,8,96,10368,108615168,11798392572168192,
%T A001697 139202068568601556987554268864512,
%U A001697 19377215893777651167043206536157390321290709180447278572301746176
%N A001697 a(n+1) = a(n)(a(0) + ... + a(n)).
%C A001697 Number of binary trees of height n where for each node the left subtree is at least as high as the right subtree. - _Franklin T. Adams-Watters_, Feb 08 2007
%C A001697 The next term (a(10)) has 129 digits. - _Harvey P. Dale_, Jan 24 2016
%C A001697 Number of plane trees where the root has exactly n children and the i-th child of any node has at most i-1 children. - _David Eppstein_, Dec 18 2021
%D A001697 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001697 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001697 John Cerkan, <a href="/A001697/b001697.txt">Table of n, a(n) for n = 0..12</a>
%H A001697 A. V. Aho and N. J. A. Sloane, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
%H A001697 A. V. Aho and N. J. A. Sloane, <a href="/A000058/a000058.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
%H A001697 Daniel Duverney, Takeshi Kurosawa, Iekata Shiokawa, <a href="https://arxiv.org/abs/1912.12565">Transformation formulas of finite sums into continued fractions</a>, arXiv:1912.12565 [math.NT], 2019.
%H A001697 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%H A001697 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A001697 a(n) ~ c^(2^n), where c = 1.3352454783981919948826893254756974184778316104856161827213437094446034867599... . - _Vaclav Kotesovec_, May 21 2015
%t A001697 a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 1]^2*(1 + 1/a[n - 2]); Table[a[n], {n, 0, 9}] (* _Jean-François Alcover_, Jul 02 2013 *)
%t A001697 nxt[{t_,a_}]:={t+t*a,t*a}; Transpose[NestList[nxt,{1,1},10]][[2]] (* _Harvey P. Dale_, Jan 24 2016 *)
%o A001697 (PARI) a(n)=if(n<2,n >= 0,a(n-1)^2*(1+1/a(n-2)))
%o A001697 (Haskell)
%o A001697 a001697 n = a001697_list !! n
%o A001697 a001697_list = 1 : 1 : f [1,1] where
%o A001697 f xs@(x:_) = y : f (y : xs) where y = x * sum xs
%o A001697 -- _Reinhard Zumkeller_, Apr 29 2013
%o A001697 (Magma) [n le 2 select 1 else Self(n-1)^2*(1+1/Self(n-2)): n in [1..12]]; // _Vincenzo Librandi_, Nov 25 2015
%Y A001697 a(n) = A039941(2*n+1); first differences of A001696 give this sequence.
%Y A001697 Cf. A002658, A001699.
%Y A001697 Cf. A064847.
%K A001697 nonn,easy,nice
%O A001697 0,3
%A A001697 _N. J. A. Sloane_
%E A001697 Additional comments from _Michael Somos_, May 19 2000