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.
%I A043303 #27 Jan 03 2025 23:29:56
%S A043303 1,1,1,1,43867,77683,657931,1723168255201,151628697551,
%T A043303 154210205991661,1520097643918070802691,25932657025822267968607,
%U A043303 19802288209643185928499101,29149963634884862421418123812691,2913228046513104891794716413587449,396793078518930920708162576045270521
%N A043303 Numerator of B(4n+2)/(2n+1) where B(m) are the Bernoulli numbers.
%C A043303 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 A043303 Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Infinite series, p. 262.
%H A043303 Seiichi Manyama, <a href="/A043303/b043303.txt">Table of n, a(n) for n = 0..156</a>
%F A043303 B(4*n+2)/(8*n+4) = Sum_{k>=1} k^(4*n+1)/(exp(2*Pi*k)-1).
%F A043303 a(n) = A001067(2n+1).
%p A043303 seq(numer(bernoulli(4*n+2)/(2*n+1)),n=0..30); # _Robert Israel_, Sep 18 2016
%t A043303 Table[BernoulliB[4n+2]/(2n+1),{n,0,20}]//Numerator (* _Harvey P. Dale_, Aug 13 2018 *)
%o A043303 (PARI) a(n)=if(n<0,0,numerator(bernfrac(4*n+2)/(2*n+1)))
%Y A043303 Cf. A001067, A043304.
%K A043303 easy,frac,nonn
%O A043303 0,5
%A A043303 _Benoit Cloitre_, Apr 04 2002