

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
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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. 7737.
Eric Weisstein's World of Mathematics, Circle Line Picking
Eric Weisstein's World of Mathematics, Gamma Function


FORMULA

a(n) = denominator of binomial(2*n1/2, 1/2).
a(n) are denominators of coefficients of 1/(sqrt(1+x)sqrt(1x)) 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*n1/2, 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*n1/2, 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



