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A061549
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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.
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7
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
We observe that b(n) = ln(a(n))/ln(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.
(End)
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REFERENCES
| Kozelka, Robert M. "Grade Point Averages and the Central Limit Theorem." American Mathematical Monthly. Nov. 1979 (86:9) pp. 773-7.
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LINKS
| Eric Weisstein's World of Mathematics, Circle Line Picking
Eric Weisstein's World of Mathematics, Gamma Function
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FORMULA
| a(n) = 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 (benoit7848c(AT)orange.fr), Mar 12 2002
a(n)=16^n/A001316(n); - Paul Barry (pbarry(AT)wit.ie), Jun 29 2006
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
a(n) = denom((4*n)!/(2^(4*n)*(2*n)!^2))
(End)
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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.
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MAPLE
| seq(denom(binomial(2*n-1/2, -1/2)), n=1..20);
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CROSSREFS
| Cf. A061548.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 06 2009: (Start)
Equals abs(A067624(n)/A117972(n))
Bisection of A046161.
Appears in A162448.
(End)
Sequence in context: A171755 A204194 A093586 * A105094 A036294 A133680
Adjacent sequences: A061546 A061547 A061548 * A061550 A061551 A061552
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KEYWORD
| nonn,frac,easy
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AUTHOR
| Leah Schmelzer (leah2002(AT)mit.edu), May 16 2001
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EXTENSIONS
| More terms from Asher Auel (asher.auel(AT)reed.edu), May 20 2001
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