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 A270121 Denominators in a perturbed Engel series. 4
 7, 112, 403200, 1755760043520000, 53695136666462381094317154204367872000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sum of the series 6/a(1)+1/a(2)+1/a(3)+... is a transcendental number, and has a continued fraction expansion whose coefficients are given explicitly in terms of the sequence a(n) and the ratios a(n+1)/a(n). LINKS Amiram Eldar, Table of n, a(n) for n = 1..8 Andrew N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.8.4. Andrew N. W. Hone, Continued fractions for some transcendental numbers, arXiv:1509.05019 [math.NT], 2015-2016, Monatsh. Math. DOI: 10.1007/s00605-015-0844-2. FORMULA The sequence is generated by taking a(n+1)=b(n-1)*a(n)*(1+n*a(n)), b(n)=a(n+1)/a(n) for n>=1 with initial values a(1)=7,b(0)=2. Alternatively, if a(1)=7,a(2)=112 are given then a(n+1)*a(n-1)=a(n)^2*(1+n*a(n)) for n>=2. Sum_{n>=1} 1/a(n) = -5/7 + A270137. - Amiram Eldar, Nov 20 2020 MATHEMATICA a[1] = 7; a[2] = 112; a[n_] := a[n] = (a[n-1]^2 (1+(n-1)a[n-1]))/a[n-2]; Array[a, 5] (* Jean-François Alcover, Dec 16 2018 *) CROSSREFS Cf. A112373, A114552, A114550, A270137. Sequence in context: A010795 A293456 A099153 * A079296 A081531 A142537 Adjacent sequences:  A270118 A270119 A270120 * A270122 A270123 A270124 KEYWORD nonn AUTHOR Andrew Hone, Mar 11 2016 STATUS approved

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Last modified April 21 10:25 EDT 2021. Contains 343148 sequences. (Running on oeis4.)