OFFSET
0,2
COMMENTS
From the von Staudt-Clausen theorem it follows that a(n) can be computed without using Bernoulli polynomials or the 'denominator'-function (see the Sage implementation). - Peter Luschny, Mar 24 2014
REFERENCES
J. R. Philip, The symmetrical Euler-Maclaurin summation formula, Math. Sci., 6, 1981, pp. 35-41.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..250
Eric Weisstein's World of Mathematics, von Staudt-Clausen Theorem.
FORMULA
a(n) = denominator(2*(2*Pi)^(-2*n)*(2*n)!*Li_{2*n}(-1)). - Peter Luschny, Jun 29 2012
Apparently, denominators of the fractions with e.g.f. (x/2) / sinh(x/2). - Tom Copeland, Sep 17 2016
MAPLE
with(numtheory); seq(denom(bernoulli(2*n, 1/2)), n=0..20);
MATHEMATICA
Table[ BernoulliB[2*n, 1/2] // Denominator, {n, 0, 18}] (* Jean-François Alcover, Apr 15 2013 *)
a[ n_] := If[ n < 0, 0, (2 n)! SeriesCoefficient[ x/2 / Sinh[x/2], {x, 0, 2 n}] // Denominator]; (* Michael Somos, Sep 21 2016 *)
PROG
(PARI) a(n)=denominator(subst(bernpol(2*n, x), x, 1/2)); \\ Joerg Arndt, Apr 17 2013
(Sage)
def A033469(n):
if n == 0: return 1
M = map(lambda i: i+1, divisors(2*n))
return 2^(2*n-1)*mul(filter(lambda s: is_prime(s), M))
[A033469(n) for n in (0..21)] # Peter Luschny, Mar 24 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Joerg Arndt, Apr 17 2013
STATUS
approved