A259644 - OEIS

%I #15 Dec 13 2023 08:45:49

%S 1,2,5,31,2419,176795035,883922739668546300971,

%T 1511516294872733607299090320742127160367108420362968907

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

%H Reinhard Zumkeller, <a href="/A259644/b259644.txt">Table of n, a(n) for n = 0..10</a>

%H Andrew N. W. Hone, <a href="http://list.seqfan.eu/oldermail/seqfan/2015-July/015015.html">Update on A112373</a>, SeqFan list, July 02 2015.

%H 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 Sum(1/A112373(k)) = 1, 2, 5/2, 31/12, 2419/936, 176795035/68408496, ...

%t (* b = A112373 *)

%t b[n_] := b[n] = If[n < 2, 1, (b[n-1]^3 + b[n-1]^2)/b[n-2]];

%t a[n_] := Sum[1/b[k], {k, 0, n}] // Numerator;

%t Table[a[n], {n, 0, 7}] (* _Jean-François Alcover_, Dec 15 2018 *)

%o (Haskell)

%o import Data.Ratio (numerator)

%o a259644 n = a259644_list !! n

%o a259644_list = map numerator $

%o                scanl1 (+) $ map (recip . fromIntegral) a112373_list

%Y Cf. A112373.

%K nonn,frac

%O 0,2

%A _Reinhard Zumkeller_, Jul 02 2015