OFFSET
0,2
COMMENTS
Sum_{i>=0} i/2^i = 2. - Alonso del Arte, Aug 15 2012
REFERENCES
C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 95.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.
FORMULA
a(n) = denominator(2-(n+2)/2^n). - Sean A. Irvine, Oct 25 2020
Denominators of coefficients in expansion of 2*x / ((1 - x) * (2 - x)^2). - Ilya Gutkovskiy, Aug 04 2023
EXAMPLE
a(4) = 8 because 1/2 + 2/4 + 3/8 + 4/16 = 1/2 + 1/2 + 3/8 + 1/4 = 1 + 5/8 = 13/8.
MAPLE
seq(denom(2-(n+2)/2^n), n=0..50); # Ridouane Oudra, Jul 16 2023
MATHEMATICA
Table[Denominator[Sum[i/2^i, {i, n}]], {n, 40}] (* Alonso del Arte, Aug 08 2012 *)
PROG
(PARI) concat(1, vector(100, n, denominator(sum(i=1, n, i/2^i)))) \\ Colin Barker, Nov 09 2014
(PARI) a(n) = denominator(2-(n+2)/2^n); \\ Joerg Arndt, Jul 17 2023
(Magma) [1] cat [Denominator(&+[i/2^i: i in [1..n]]): n in [1..40]]; // Vincenzo Librandi, Nov 09 2014
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved