OFFSET
1,4
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 numerators of the coefficients t1, t2, t3, ... are given by this sequence.
The sequence is different from A002425, but the first difference is at index 60 (see the text files).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..275 (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) = numerator((1-4^(-n))*Bernoulli(2*n)/(n*(2*n-1))).
EXAMPLE
For n = 4, a(4) = numerator(-17/13336) = -17.
MATHEMATICA
Table[Numerator[(1 - 4^(-n)) BernoulliB[2 n] / (n (2 n - 1))], {n, 30}] (* Vincenzo Librandi, Sep 15 2016 *)
PROG
(Magma) [Numerator((4^n-1)*BernoulliNumber(2*n)/4^n/n/(2*n-1)): n in [1..20]];
(PARI) a(n) = numerator((1-4^(-n))*bernfrac(2*n)/(n*(2*n-1))); \\ Joerg Arndt, Sep 14 2016
CROSSREFS
KEYWORD
frac,sign
AUTHOR
Richard P. Brent, Sep 13 2016
STATUS
approved