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A259644 Numerators of sum(1/A112373(k): k=0..n), denominators = A112373.

%I A259644 #16 Dec 23 2024 14:53:44
%S A259644 1,2,5,31,2419,176795035,883922739668546300971,
%T A259644 1511516294872733607299090320742127160367108420362968907
%N A259644 Numerators of sum(1/A112373(k): k=0..n), denominators = A112373.
%H A259644 Reinhard Zumkeller, <a href="/A259644/b259644.txt">Table of n, a(n) for n = 0..10</a>
%H A259644 Andrew N. W. Hone, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-July/015015.html">Update on A112373</a>, SeqFan list, July 02 2015.
%H A259644 Andrew N. W. Hone, <a href="http://arxiv.org/abs/1507.00063">Curious continued fractions, nonlinear recurrences and transcendental numbers</a>, arXiv:1507.00063 [math.NT], 2015.
%e A259644 Sum(1/A112373(k)) = 1, 2, 5/2, 31/12, 2419/936, 176795035/68408496, ...
%t A259644 (* b = A112373 *)
%t A259644 b[n_] := b[n] = If[n < 2, 1, (b[n-1]^3 + b[n-1]^2)/b[n-2]];
%t A259644 a[n_] := Sum[1/b[k], {k, 0, n}] // Numerator;
%t A259644 Table[a[n], {n, 0, 7}] (* _Jean-François Alcover_, Dec 15 2018 *)
%o A259644 (Haskell)
%o A259644 import Data.Ratio (numerator)
%o A259644 a259644 n = a259644_list !! n
%o A259644 a259644_list = map numerator $
%o A259644                scanl1 (+) $ map (recip . fromIntegral) a112373_list
%Y A259644 Cf. A112373.
%K A259644 nonn,frac
%O A259644 0,2
%A A259644 _Reinhard Zumkeller_, Jul 02 2015