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 A174864 a(1) = 1, a(n) = square of the sum of previous terms. 5
 1, 1, 4, 36, 1764, 3261636, 10650053687364, 113423713055411194304049636, 12864938683278671740537145884937248491231415124195364 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) divides a(n+1) with result a square. Except for first two terms, partial sum k of a(n) is divisible by 6. These numbers are divisible by their digital roots, which makes the sequence a subsequence of A064807. - Ivan N. Ianakiev, Oct 09 2013 a(n) is the number of binary trees in which the nodes are labeled by non-negative integer heights, the left and right children of each node (if present) must have smaller height, and the root has height n-2. For instance there are four trees with root height 1: the left and right children of the root may or may not be present, and must each be at height 0 if present. - David Eppstein, Oct 25 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..13 FORMULA a(n+1) = [Sum_{i=1..n}{a(i)}]^2, with a(1)=1. - Paolo P. Lava, Apr 23 2010 a(n+1) = (a(n) + sqrt(a(n)))^2 = a(n) * (sqrt(a(n)) + 1)^2 for n > 1. - Charles R Greathouse IV, Jun 30 2011 a(n) = A000058(n-1) - A000058(n-2), n>=2. - Ivan N. Ianakiev, Oct 09 2013 MAPLE P:=proc(i) local a, s, n; a:=1; print(1); s:=1; for n from 0 by 1 to i do a:=s^2; print(a); s:=s+a; od; end: P(10); # Paolo P. Lava, Apr 23 2010 MATHEMATICA t = {1}; Do[AppendTo[t, Total[t]^2], {n, 9}]; t (* Vladimir Joseph Stephan Orlovsky, Feb 24 2012 *) Join[{1}, FoldList[(#+Sqrt[#])^2&, 1, Range[7]]] (* Ivan N. Ianakiev, May 08 2015 *) PROG (PARI) a=vector(10); a[1]=a[2]=1; for(n=3, #a, a[n]=a[n-1]*(sqrtint(a[n-1])+1)^2); a CROSSREFS Cf. A000058, A007018. Sequence in context: A143764 A152287 A086857 * A175493 A179870 A001152 Adjacent sequences:  A174861 A174862 A174863 * A174865 A174866 A174867 KEYWORD easy,nonn AUTHOR Giovanni Teofilatto, Mar 31 2010 STATUS approved

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Last modified January 21 13:28 EST 2019. Contains 319350 sequences. (Running on oeis4.)