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 A001697 a(n+1) = a(n)(a(0) + ... + a(n)). (Formerly M1902 N0751) 5
 1, 1, 2, 8, 96, 10368, 108615168, 11798392572168192, 139202068568601556987554268864512, 19377215893777651167043206536157390321290709180447278572301746176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 The next term (a(10)) has 129 digits. - Harvey P. Dale, Jan 24 2016 Number of plane trees where the root has exactly n children and the ith child of any node has at most i-1 children. - David Eppstein, Dec 18 2021 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS John Cerkan, Table of n, a(n) for n = 0..12 A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link. Daniel Duverney, Takeshi Kurosawa, Iekata Shiokawa, Transformation formulas of finite sums into continued fractions, arXiv:1912.12565 [math.NT], 2019. FORMULA a(n) ~ c^(2^n), where c = 1.3352454783981919948826893254756974184778316104856161827213437094446034867599... . - Vaclav Kotesovec, May 21 2015 MATHEMATICA a = 1; a = 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 *) nxt[{t_, a_}]:={t+t*a, t*a}; Transpose[NestList[nxt, {1, 1}, 10]][] (* Harvey P. Dale, Jan 24 2016 *) PROG (PARI) a(n)=if(n<2, n >= 0, a(n-1)^2*(1+1/a(n-2))) (Haskell) a001697 n = a001697_list !! n a001697_list = 1 : 1 : f [1, 1] where    f xs@(x:_) = y : f (y : xs) where y = x * sum xs -- Reinhard Zumkeller, Apr 29 2013 (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 CROSSREFS a(n) = A039941(2*n+1); first differences of A001696 give this sequence. Cf. A002658, A001699. Cf. A064847. Sequence in context: A001417 A156926 A326866 * A006069 A270485 A223042 Adjacent sequences:  A001694 A001695 A001696 * A001698 A001699 A001700 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Additional comments from Michael Somos, May 19 2000 STATUS approved

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Last modified July 7 02:44 EDT 2022. Contains 355141 sequences. (Running on oeis4.)