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 A111130 #15 Sep 08 2022 08:45:20
%S A111130 3,11,295,18839,2178311,396789539,104534716847,37582455061871,
%T A111130 17677524703000879,10535586945520548779,7758255095720238886679,
%U A111130 6916955444929558486935047,7342438845112941396534404087,9150463033951198007724075565619,13229286823498332297225524829163231
%N A111130 Numerator of (n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n.
%C A111130 (n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n converges very rapidly to e.
%C A111130 These can be prime, as is the case for a(0) = 3, a(1) = 11, a(4) = 18839, a(8) = 37582455061871. These are always odd, just as all but the first denominator of A090205 is even. - _Jonathan Vos Post_, Oct 19 2005
%H A111130 G. C. Greubel, <a href="/A111130/b111130.txt">Table of n, a(n) for n = 0..210</a>
%H A111130 H. J. Brothers and J. A. Knox, <a href="http://www.brotherstechnology.com/docs/mi_paper1.pdf">New closed-form approximations to the logarithmic constant e</a>, Math. Intelligencer, 20 (1998), 25-29.
%e A111130 3, 11/4, 295/108, 18839/6912, 2178311/800000, 396789539/145800000, 104534716847/38423222208, ...
%t A111130 Join[{3}, Numerator[Table[(n + 2)^(n + 2)/(n + 1)^(n + 1) - (n + 1)^(n + 1)/n^n, {n, 1, 25}]]] (* _G. C. Greubel_, Apr 09 2018 *)
%o A111130 (PARI) a(n) = numerator((n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n); \\ _Michel Marcus_, Jun 27 2015
%o A111130 (Magma) [Numerator((n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n): n in [0..30]]; // _G. C. Greubel_, Apr 09 2018
%Y A111130 Denominators are 1, 4, 108, 6912, ... - see A090205.
%K A111130 nonn,frac
%O A111130 0,1
%A A111130 _N. J. A. Sloane_, Oct 17 2005