OFFSET
0,2
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..500
Robert M. Kozelka, Grade Point Averages and the Central Limit Theorem, American Mathematical Monthly. Nov. 1979 (86:9) pp. 773-7.
FORMULA
a(n) = numerator(binomial(2*n-1/2, -1/2)).
From Johannes W. Meijer, Jul 06 2009: (Start)
a(n) = numerator((4*n)!/(2^(4*n)*(2*n)!^2)).
a(n) is the numerator of the coefficient of power series in x around x=0 of sqrt(1 + sqrt(1 - x))/(sqrt(2)*sqrt(1 - x)). - Karol A. Penson, Apr 16 2018
EXAMPLE
For n=1, the binomial(2*n-1/2, -1/2) yields the term 3/8. The numerator of this term is 3, which is the second term of the sequence.
MAPLE
seq(numer(binomial(2*n-1/2, -1/2)), n=0..20);
MATHEMATICA
Table[Numerator[(4*n) !/(2^(4*n)*(2*n) !^2) ], {n, 0, 20}] (* Indranil Ghosh, Mar 11 2017 *)
Table[Numerator[SeriesCoefficient[Series[(Sqrt[1 + Sqrt[1 - x]]/Sqrt[2 - 2* x]), {x, 0, n}], n]], {n, 0, 20}]. (* Karol A. Penson, Apr 16 2018 *)
PROG
(Sage)
def A061548(n): return binomial(4*n, 2*n)/2^sum(n.digits(2))
[A061548(n) for n in (0..20)] # Peter Luschny, Mar 23 2014
(PARI) for(n=0, 20, print1(numerator((4*n)!/(2^(4*n)*(2*n)!^2)), ", ")) \\ Indranil Ghosh, Mar 11 2017
(Python)
import math
from fractions import gcd
f = math.factorial
def A061548(n): return f(4*n) / gcd(f(4*n), (2**(4*n)*f(2*n)**2)) # Indranil Ghosh, Mar 11 2017
(Magma)
A061548:= func< n | Numerator(Binomial(4*n, 2*n)/4^n) >;
[A061548(n): n in [0..25]]; // G. C. Greubel, Oct 19 2024
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Leah Schmelzer (leah2002(AT)mit.edu), May 16 2001
EXTENSIONS
More terms from Asher Auel, May 20 2001
STATUS
approved