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

1, 2, 5, 31, 2419, 176795035, 883922739668546300971, 1511516294872733607299090320742127160367108420362968907

Offset: 0

Author

Reinhard Zumkeller, Jul 02 2015

Keywords

• nonn
• frac

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10
• Andrew N. W. Hone, Update on A112373, SeqFan list, July 02 2015.
• Andrew N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, arXiv:1507.00063 [math.NT], 2015.

Crossrefs

Cf. A112373.

Programs

Haskell

import Data.Ratio (numerator)
a259644 n = a259644_list !! n
a259644_list = map numerator $
               scanl1 (+) $ map (recip . fromIntegral) a112373_list

Mathematica

(* b = A112373 *)
b[n_] := b[n] = If[n < 2, 1, (b[n-1]^3 + b[n-1]^2)/b[n-2]];
a[n_] := Sum[1/b[k], {k, 0, n}] // Numerator;
Table[a[n], {n, 0, 7}] (* Jean-François Alcover, Dec 15 2018 *)