OFFSET
1,1
COMMENTS
The sequence shares numerators with the Harary numbers, A160050.
This is the sequence 1/2 + 1/3 + 1/4 +...+1/n using relativistic velocity addition, where the addition of velocities a and b = (a+b) / (1 + a*b/c^2). That is, for objects traveling at c/2 + c/3 + ... +c/n relative to each other, the n-th object has velocity A160050(n)/a(n)*c relative to a stationary observer.
LINKS
Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Ulam Spiral of the first 4000 terms.
Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).
FORMULA
G.f.: -x*(x^8-2*x^7+4*x^6-6*x^5+7*x^4-3*x^3+2*x^2+x+2) / ((x-1)^3*(x^2+1)^3). - Colin Barker, Jul 18 2015
EXAMPLE
a(10) = a(9) + 1/11 using relativistic velocity addition. Since a(9) = 27/28, the sum is (27/28 + 1/11) / (1 + 27/28 * (1/11)) = (325 / 308) / (335/308) = 65/67.
PROG
(R) library(gmp); reladd<-function(x, y) (x+y)/(1+x*y)y=as.bigq(rep(1, 100)); y[1]=y[1]/2; for(i in 2:100) y[i]=reladd(y[i-1], y[i]/(i+1)); denominator(y)
(PARI) Vec(-x*(x^8-2*x^7+4*x^6-6*x^5+7*x^4-3*x^3+2*x^2+x+2) / ((x-1)^3*(x^2+1)^3) + O(x^100)) \\ Colin Barker, Jul 18 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved