cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A014509 Truncation of Bernoulli number: floor(|B_2n|) * sign(B_2n).

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%I A014509 #30 Nov 13 2018 03:17:44
%S A014509 1,0,0,0,0,0,0,1,-7,54,-529,6192,-86580,1425517,-27298231,601580873,
%T A014509 -15116315767,429614643061,-13711655205088,488332318973593,
%U A014509 -19296579341940068,841693047573682615,-40338071854059455413,2115074863808199160560,-120866265222965259346027
%N A014509 Truncation of Bernoulli number: floor(|B_2n|) * sign(B_2n).
%D A014509 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.
%H A014509 Robert Israel, <a href="/A014509/b014509.txt">Table of n, a(n) for n = 0..317</a>
%H A014509 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A014509 <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>
%F A014509 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
%p A014509 f:= proc(n) local b; b:= bernoulli(2*n);
%p A014509 floor(abs(b))*signum(b)
%p A014509 end proc:
%p A014509 map(f, [$0..30]); # _Robert Israel_, Nov 12 2018
%t A014509 Table[Sign@BernoulliB[2n] Floor@Abs@BernoulliB[2n], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 12 2015 *)
%o A014509 (PARI) a(n) = my(b=bernfrac(2*n)); floor(abs(b))*sign(b); \\ _Michel Marcus_, Nov 13 2018
%Y A014509 Cf. A134825.
%K A014509 sign
%O A014509 0,9
%A A014509 _Simon Plouffe_
%E A014509 Entry revised by _Franklin T. Adams-Watters_, Sep 14 2005