OFFSET
0,5
REFERENCES
Glaisher, J. W. L.; Tables of the first 250 Bernoulli numbers. Trans. Cambridge Phil. Soc. 12 (1873), 384-391.
Peters, J. and Stein, J., Matematische Tafeln. Revised Russian Edition, 1968, Moscow.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Maths StackExchange, Bernoulli numbers and Pi^2, 2019.
FORMULA
a(n) = floor( (n+1)*(2*n+1)/(2*Pi^2)) (conjectured). - Bill McEachen, Dec 08 2021
A002939(n+1)*B(2*n)/B(2*(n+1)) = -(2*Pi)^2*(1 + O(1/4^n)). See the StackExchange link. - Peter Luschny, Dec 08 2021
EXAMPLE
a(3) = floor(abs(B(4)/B(3))) = floor((1/30)/(1/42)) = floor(7/5) = floor(1.4) = 1.
a(249) = floor(abs(B(250)/B(249))) = 6319.
MAPLE
seq(floor(abs(bernoulli(2*n+2)/bernoulli(2*n))), n=0..200); # Robert Israel, Jun 27 2018
MATHEMATICA
Table[Floor[Abs[BernoulliB[2*n + 2]/BernoulliB[2*n]]], {n, 0, 60}] (* T. D. Noe, Jun 27 2013 *)
PROG
(PARI) a(n) = floor(abs(bernfrac(2*n+2)/bernfrac(2*n))) \\ Michel Marcus, Jun 27 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved