OFFSET
1,6
COMMENTS
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 257, Eq. 6.1.41.
L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..314
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 257, Eq. 6.1.41.
R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, arXiv:1608.04834 [math.NA], 2016.
N. Elezovic, Asymptotic Expansions of Central Binomial Coefficients and Catalan Numbers, J. Int. Seq. 17 (2014) # 14.2.1.
Eric Weisstein's World of Mathematics, Stirling's Series
FORMULA
From numerator of Jk(z) = (-1)^(k-1)*Bk/(((2k)*(2k-1))*z^(2k-1)), so Gamma(z) = sqrt(2*Pi)*z^(z-0.5)*exp(-z)*exp(J(z)).
MAPLE
seq(numer(bernoulli(2*n)/(2*n*(2*n-1))), n = 1..25); # G. C. Greubel, Sep 19 2019
MATHEMATICA
Table[ Numerator[ BernoulliB[2n]/(2n(2n - 1))], {n, 1, 22}] (* Robert G. Wilson v, Feb 03 2004 *)
s = LogGamma[z] + z - (z - 1/2) Log[z] - Log[2 Pi]/2 + O[z, Infinity]^42; DeleteCases[CoefficientList[s, 1/z], 0] // Numerator (* Jean-François Alcover, Jun 13 2017 *)
PROG
(PARI) a(n)=if(n<1, 0, numerator(bernfrac(2*n)/(2*n)/(2*n-1)))
(Magma) [Numerator(Bernoulli(2*n)/(2*n*(2*n-1))): n in [1..25]]; // G. C. Greubel, Sep 19 2019
(Sage) [numerator(bernoulli(2*n)/(2*n*(2*n-1))) for n in (1..25)] # G. C. Greubel, Sep 19 2019
(GAP) List([1..25], n-> NumeratorRat(Bernoulli(2*n)/(2*n*(2*n-1))) ); # G. C. Greubel, Sep 19 2019
CROSSREFS
KEYWORD
frac,sign,nice
AUTHOR
Douglas Stoll (dougstoll(AT)email.msn.com)
EXTENSIONS
More terms from Frank Ellermann, Jun 13 2001
STATUS
approved