A003414 - OEIS

%I #24 Oct 21 2023 19:51:09

%S -1,0,-1,0,-1,0,-1,0,-2,13,-141,1803,-27414,487468,-10026348,

%T 236192433,-6317862398,190439655626,-6425425249653,241207241774250,

%U -10020155328258127,458387180159766538,-22989944171828251746,1259023596072554784854,-75008667460769643668558

%N a(n) = floor( Bernoulli(2*n)/(-4*n) ).

%D F. Hirzebruch et al., Manifolds and Modular Forms, Vieweg, 2nd ed. 1994, p. 130.

%D D. C. Ravenel, Complex cobordism theory for number theorists, Lecture Notes in Mathematics, 1326, Springer-Verlag, Berlin-New York, 1988, pp. 123-133.

%H T. D. Noe, <a href="/A003414/b003414.txt">Table of n, a(n) for n = 1..100</a>

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.

%e a(10) = 13 because the 20th (2 * 10) Bernoulli number is -174611/330, and that divided by (-4) * 10 is approximately 13.2281.

%t Table[Floor[BernoulliB[2n]/(-4n)], {n, 24}] (* _Alonso del Arte_, Jul 11 2012 *)

%Y Cf. A000367/A002445.

%K sign

%O 1,9

%A _N. J. A. Sloane_