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 A273196 #15 Mar 08 2020 10:14:10
%S A273196 1,-1,37,-6833,56377,-439772603,27217772209,-202070742359,
%T A273196 80837575181815013,-155957202651688954367,1770963292969902374951,
%U A273196 -16092436217742770647634507,2975968726866580246152132993,-963399772945511487665759472653,3891037048609240492066339458106680163
%N A273196 a(n) = numerator of T(n, 2) with T(n, m) = Sum_{k=0..n}( 1/(m*k+1) * Sum_{j=0..m*k} (-1)^j*C(k,j)*j^(m*n) ).
%C A273196 T(n,0) are the natural numbers, T(n,1) the Bernoulli numbers.
%t A273196 Table[Function[{n, m}, If[n == 0, 1, Numerator@ Sum[1/(m k + 1) Sum[(-1)^j Binomial[k, j] j^(m n), {j, 0, m k}], {k, 0, n}]]][n, 2], {n, 0, 14}] (* _Michael De Vlieger_, Jun 26 2016 *)
%o A273196 (Sage)
%o A273196 def T(n, m): return sum(1/(m*k+1)*sum((-1)^j*binomial(k,j)*j^(m*n) for j in (0..m*k)) for k in (0..n))
%o A273196 def a(n): return T(n, 2).numerator()
%o A273196 print([a(n) for n in (0..14)])
%Y A273196 Cf. A273197 (denominator), T(n,0) = A000027, T(n,1) = A027641/A027642.
%Y A273196 Also T(n,1)*(1*n+1)! = A129814, T(n,2)*(2*n+1)! = A273198.
%K A273196 sign,frac
%O A273196 0,3
%A A273196 _Peter Luschny_, Jun 26 2016