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

Author

Simon Plouffe

Keywords

• sign

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.

Crossrefs

Cf. A134825.

Programs

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 *)

PARI

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

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

Extensions

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