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 A133002 #36 Sep 01 2021 11:43:49
%S A133002 1,-1,5,-1,139,-1,859,71,-9769,233,-6395527,145069,-304991568097,
%T A133002 -95164619917,119780081383,-3046785293,4002469707564917,
%U A133002 -102407337854027,1286572077762833639,219276930957009857,-20109624681057406222913,1651690537394493957719
%N A133002 Numerators of Blandin-Diaz compositional Bernoulli numbers (B^S)_1,n.
%C A133002 Denominators are A133003. "Bernoulli numbers for S are shown in the table."
%C A133002 The signs of a(0) and a(3) are wrong in table of p. 11 of Bandin article. - _Daniel Suteu_, Feb 24 2018
%H A133002 Daniel Suteu, <a href="/A133002/b133002.txt">Table of n, a(n) for n = 0..200</a>
%H A133002 Hector Blandin and Rafael Diaz, <a href="https://arxiv.org/abs/0708.0809">Compositional Bernoulli numbers</a>, arXiv:0708.0809 [math.CO], 2007-2008, p. 11, 1st table.
%F A133002 a(n) = numerator(f(n) * n!), where f(0) = 1, f(n) = -Sum_{k=0..n-1} f(k) / ((n-k+1)!)^2. - _Daniel Suteu_, Feb 23 2018
%F A133002 E.g.f. for fractions: x / (BesselI(0,2*sqrt(x)) - 1). - _Ilya Gutkovskiy_, Sep 01 2021
%e A133002 1, -1/4, 5/72, -1/48, 139/21600, -1/540, 859/2540160, 71/483840, -9769/36288000 (corrected by _Daniel Suteu_, Feb 24 2018).
%t A133002 f[0] = 1; f[n_] := f[n] = -Sum[f[k]/((n-k+1)!)^2, {k, 0, n-1}]; Table[f[n]*n! // Numerator, {n, 0, 21}] (* _Jean-François Alcover_, Feb 25 2018, after _Daniel Suteu_ *)
%Y A133002 Cf. A132092, A132093, A132094, A132095, A132096, A132097, A132098, A132099.
%Y A133002 Cf. A133000, A133001, A133003, A133004, A133005.
%K A133002 sign,frac
%O A133002 0,3
%A A133002 _Jonathan Vos Post_, Aug 09 2007
%E A133002 Corrected the sign of a(0) and a(3) by _Daniel Suteu_, Feb 24 2018
%E A133002 Terms beyond a(8) from _Daniel Suteu_, Feb 24 2018