OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..387
Wikipedia, Velocity-addition formula.
FORMULA
a(n)/A348132(n) = tanh(n * arctanh(1/n)).
a(2n-1) = n^(2n-1) - (n-1)^(2n-1) and a(2n) = ((2n+1)^(2n) - (2n-1)^(2n)) / 2. - Thomas Ordowski, Feb 12 2022
EXAMPLE
The fractions begins with 1, 4/5, 7/9, 272/353, 211/275, 51012/66637, 14197/18571, 18640960/24405761, 1690981/2215269, 11225320100/14712104501, ...
For n = 2, the sum of two velocities of 1/2 is (1/2 + 1/2)/(1 + (1/2)*(1/2)) = 4/5, thus a(2) = 4.
MATHEMATICA
f[n_] := Module[{s = 1/n}, Do[s = (s + 1/n)/(1 + s/n), {k, 1, n - 1}]; s]; Numerator @ Array[f, 20]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Amiram Eldar, Oct 01 2021
STATUS
approved