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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) # uses[A000120] 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 September 30 21:27 EDT 2020. Contains 337440 sequences. (Running on oeis4.)