OFFSET
0,3
COMMENTS
Variance here is sample variance unbiased estimator. For population variance, the denominator is A191871(n+1) = A000265(n+1)^2. - Chai Wah Wu, Mar 25 2018
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..10000
Simon Demers, Taylor's Law Holds for Finite OEIS Integer Sequences and Binomial Coefficients, American Statistician, online: 19 Jan 2018.
FORMULA
a(0) = 1; a(n) = denominator of binomial(2n,n)/n - 4^n/(n*(n+1)) for n >= 1. - Chai Wah Wu, Mar 23 2018
EXAMPLE
The first few variances are 0, 0, 1/3, 4/3, 47/10, 244/15, 1186/21, 1384/7, 25147/36, 112028/45, 98374/11, 1067720/33, 1531401/13, 39249768/91, 166656772/105, 88008656/15, 2961699667/136, 12412521388/153, 51854046982/171, 108006842264/95, 448816369361/105, ...
MAPLE
PROG
(Python)
from fractions import Fraction
from sympy import binomial
def A301279(n):
return (Fraction(int(binomial(2*n, n)))/n - Fraction(4**n)/(n*(n+1))).denominator if n > 0 else 1 # Chai Wah Wu, Mar 23 2018
(PARI) a(n) = if(n==0, 1, denominator(binomial(2*n, n)/n - 4^n/(n*(n+1)))); \\ Altug Alkan, Mar 25 2018
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Mar 18 2018
STATUS
approved