%I #20 Aug 13 2018 11:39:57
%S 1,1,1,1,43867,77683,657931,1723168255201,151628697551,
%T 154210205991661,1520097643918070802691,25932657025822267968607,
%U 19802288209643185928499101,29149963634884862421418123812691
%N Numerator of B(4n+2)/(2n+1) where B(m) are the Bernoulli numbers.
%C Note that numerator of B(2n)/n is odd so B(2n)/(2n), B(2n)/(4n), etc. have the same numerators. - _Michael Somos_, Feb 01 2004
%D Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Infinite series, p. 262.
%H Seiichi Manyama, <a href="/A043303/b043303.txt">Table of n, a(n) for n = 0..156</a>
%F B(4n+2)/(8n+4) = sum_{k>=1} k^(4n+1)/(exp(2Pi*k)-1)).
%p seq(numer(bernoulli(4*n+2)/(2*n+1)),n=0..30); # _Robert Israel_, Sep 18 2016
%t Table[BernoulliB[4n+2]/(2n+1),{n,0,20}]//Numerator (* _Harvey P. Dale_, Aug 13 2018 *)
%o (PARI) a(n)=if(n<0,0,numerator(bernfrac(4*n+2)/(2*n+1)))
%Y Cf. A043304. a(n)=A001067(2n+1).
%K easy,frac,nonn
%O 0,5
%A _Benoit Cloitre_, Apr 04 2002