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A047872 a(n) = floor(abs(B(2*n + 2)/B(2*n))) where B(n) is the n-th Bernoulli number. 1
0, 0, 0, 1, 2, 3, 4, 6, 7, 9, 11, 13, 16, 19, 22, 25, 28, 31, 35, 39, 43, 47, 52, 57, 62, 67, 72, 78, 83, 89, 95, 102, 108, 115, 122, 129, 136, 144, 152, 160, 168, 176, 185, 193, 202, 212, 221, 231, 240, 250, 260, 271, 281, 292, 303, 314, 326, 337, 349, 361, 373 (list; graph; refs; listen; history; text; internal format)
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.

Index entries for sequences related to Bernoulli numbers.

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

Cf. A034972, A034971, A002939.

Sequence in context: A249020 A258470 A248357 * A173254 A015851 A225529

Adjacent sequences:  A047869 A047870 A047871 * A047873 A047874 A047875

KEYWORD

easy,nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified January 18 06:32 EST 2022. Contains 350452 sequences. (Running on oeis4.)