A014509 - OEIS

A014509

Truncation of Bernoulli number: floor(|B_2n|) * sign(B_2n).

1, 0, 0, 0, 0, 0, 0, 1, -7, 54, -529, 6192, -86580, 1425517, -27298231, 601580873, -15116315767, 429614643061, -13711655205088, 488332318973593, -19296579341940068, 841693047573682615, -40338071854059455413, 2115074863808199160560, -120866265222965259346027

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,9

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 810.

LINKS

Robert Israel, Table of n, a(n) for n = 0..317

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].

Index entries for sequences related to Bernoulli numbers.

FORMULA

abs(a(n)) = 2*(2*n)!/(2*Pi)^(2*n)*(1-sum(k=2, m, 1/k^(2n))+O(1/m^(2n))). - Benoit Cloitre, Jan 29 2003

MAPLE

f:= proc(n) local b; b:= bernoulli(2*n);

floor(abs(b))*signum(b)

end proc:

map(f, [$0..30]); # Robert Israel, Nov 12 2018

MATHEMATICA

Table[Sign@BernoulliB[2n] Floor@Abs@BernoulliB[2n], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 12 2015 *)

PROG

(PARI) a(n) = my(b=bernfrac(2*n)); floor(abs(b))*sign(b); \\ Michel Marcus, Nov 13 2018