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A061549 Denominator of probability that there is no error when average of n numbers is computed, assuming errors of +1, -1 are possible and they each occur with p=1/4. 14
1, 8, 128, 1024, 32768, 262144, 4194304, 33554432, 2147483648, 17179869184, 274877906944, 2199023255552, 70368744177664, 562949953421312, 9007199254740992, 72057594037927936, 9223372036854775808, 73786976294838206464, 1180591620717411303424, 9444732965739290427392 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

We observe that b(n) = log(a(n))/log(2) = A120738(n). Furthermore c(n+1) = b(n+1)-b(n) = A090739(n+1) and c(n+1)-3 = A007814(n+1) for n>=0. - Johannes W. Meijer, Jul 06 2009

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.

Eric Weisstein's World of Mathematics, Circle Line Picking

Eric Weisstein's World of Mathematics, Gamma Function

FORMULA

a(n) = denominator of binomial(2*n-1/2, -1/2).

a(n) are denominators of coefficients of 1/(sqrt(1+x)-sqrt(1-x)) power series. - Benoit Cloitre, Mar 12 2002

a(n) = 16^n/A001316(n). - Paul Barry, Jun 29 2006

a(n) = denom((4*n)!/(2^(4*n)*(2*n)!^2)). - Johannes W. Meijer, Jul 06 2009

a(n) = abs(A067624(n)/A117972(n)). - Johannes W. Meijer, Jul 06 2009

EXAMPLE

For n=1, the binomial(2*n-1/2, -1/2) yields the term 3/8. The denominator of this term is 8, which is the second term of the sequence.

MAPLE

seq(denom(binomial(2*n-1/2, -1/2)), n=0..20);

MATHEMATICA

Table[Denominator[(4*n)!/(2^(4*n)*(2*n)!^2) ], {n, 0, 19}] (* Indranil Ghosh, Mar 11 2017 *)

PROG

(Sage)

def a(n): return 1 << (4*n - A000120(n))

[a(n) for n in (0..19)]  # Peter Luschny, Dec 02 2012

(PARI) for(n=0, 19, print1(denominator((4*n)!/(2^(4*n)*(2*n)!^2)), ", ")) \\ Indranil Ghosh, Mar 11 2017

(Python)

import math

from fractions import gcd

f = math.factorial

def A061549(n): return (2**(4*n)*f(2*n)**2)/ gcd(f(4*n), (2**(4*n)*f(2*n)**2)) # Indranil Ghosh, Mar 11 2017

CROSSREFS

Cf. A061548. Bisection of A046161. Appears in A162448.

Sequence in context: A302071 A301822 A302810 * A303471 A301998 A105094

Adjacent sequences:  A061546 A061547 A061548 * A061550 A061551 A061552

KEYWORD

nonn,frac,easy

AUTHOR

Leah Schmelzer (leah2002(AT)mit.edu), May 16 2001

EXTENSIONS

More terms from Asher Auel (asher.auel(AT)reed.edu), May 20 2001

STATUS

approved

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Last modified December 7 03:00 EST 2019. Contains 329836 sequences. (Running on oeis4.)