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A275995 Denominators of coefficients in the asymptotic expansion of the logarithm of the central binomial coefficient. 2
8, 192, 640, 14336, 18432, 180224, 425984, 15728640, 8912896, 79691776, 176160768, 3087007744, 3355443200, 28991029248, 62277025792, 4260607557632, 1133871366144, 9620726743040, 20340965113856, 343047627866112, 360639813910528, 3025855999639552, 6333186975989760, 211669182486413312 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

The numerators are sequence A275994.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500 (terms 1..64 from Richard P. Brent)

R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, arXiv:1608.04834  [math.NA], 2016.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

(PARI) a(n) = denominator((1-4^(-n))*bernfrac(2*n)/(n*(2*n-1))); \\ Joerg Arndt, Sep 14 2016

CROSSREFS

Numerators are sequence A275994.

Sequence in context: A177147 A251669 A158654 * A129004 A267948 A189537

Adjacent sequences:  A275992 A275993 A275994 * A275996 A275997 A275998

KEYWORD

nonn,frac

AUTHOR

Richard P. Brent, Sep 13 2016

STATUS

approved

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Last modified October 14 07:31 EDT 2019. Contains 327995 sequences. (Running on oeis4.)