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

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

Crossrefs

Cf. A134825.

Sequence in context: A152108 A093742 A291703 * A228415 A084065 A200140

Adjacent sequences: A014506 A014507 A014508 * A014510 A014511 A014512

Keyword

sign

Author

Simon Plouffe

Extensions

Entry revised by Franklin T. Adams-Watters, Sep 14 2005

Status

approved