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A259644 Numerators of sum(1/A112373(k)): k=0..n), denominators = A112373. 2
1, 2, 5, 31, 2419, 176795035, 883922739668546300971, 1511516294872733607299090320742127160367108420362968907 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

EXAMPLE

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

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-Fran├žois Alcover, Dec 15 2018 *)

PROG

(Haskell)

import Data.Ratio (numerator)

a259644 n = a259644_list !! n

a259644_list = map numerator $

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

CROSSREFS

Cf. A112373.

Sequence in context: A080582 A064845 A295391 * A132527 A182327 A032504

Adjacent sequences:  A259641 A259642 A259643 * A259645 A259646 A259647

KEYWORD

nonn,frac

AUTHOR

Reinhard Zumkeller, Jul 02 2015

STATUS

approved

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Last modified November 29 23:27 EST 2020. Contains 338780 sequences. (Running on oeis4.)