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A275995 Denominators of coefficients in the asymptotic expansion of the logarithm of the central binomial coefficient. 2

%I

%S 8,192,640,14336,18432,180224,425984,15728640,8912896,79691776,

%T 176160768,3087007744,3355443200,28991029248,62277025792,

%U 4260607557632,1133871366144,9620726743040,20340965113856,343047627866112,360639813910528,3025855999639552,6333186975989760,211669182486413312

%N Denominators of coefficients in the asymptotic expansion of the logarithm of the central binomial coefficient.

%C -log(binomial(2n,n)) + log(4^n/sqrt(Pi*n)) has an asymptotic expansion

%C (t1/n + t2/n^3 + t3/n^5 + ...) where the denominators of the coefficients t1, t2, t3, ... are given by this sequence.

%C The numerators are sequence A275994.

%H G. C. Greubel, <a href="/A275995/b275995.txt">Table of n, a(n) for n = 1..500</a> (terms 1..64 from Richard P. Brent)

%H R. P. Brent, <a href="http://arxiv.org/abs/1608.04834">Asymptotic approximation of central binomial coefficients with rigorous error bounds</a>, arXiv:1608.04834 [math.NA], 2016.

%F a(n) = denominator((1-4^(-n))*Bernoulli(2*n)/(n*(2*n-1))).

%e For n = 4, a(4) = denominator(-17/13336) = 13336.

%t Table[Denominator[(1 - 4^(-n)) BernoulliB[2 n]/(n*(2*n - 1))], {n, 50}] (* _G. C. Greubel_, Feb 15 2017 *)

%o (MAGMA) [Denominator((4^n-1)*BernoulliNumber(2*n)/4^n/n/(2*n-1)): n in [1..30]];

%o (PARI) a(n) = denominator((1-4^(-n))*bernfrac(2*n)/(n*(2*n-1))); \\ _Joerg Arndt_, Sep 14 2016

%Y Numerators are sequence A275994.

%K nonn,frac

%O 1,1

%A _Richard P. Brent_, Sep 13 2016

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Last modified October 28 17:55 EDT 2021. Contains 348329 sequences. (Running on oeis4.)