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 A293116 #34 Oct 04 2023 13:13:01
%S A293116 1,-1,-1,-1,1,19,151,1091,7841,56519,396271,2442439,7701409,
%T A293116 -145269541,-4833158329,-104056218421,-2002667085119,-37109187217649,
%U A293116 -679877731030049,-12440309297451121,-227773259993414719,-4155839606711748061,-74724654677947488521
%N A293116 Expansion of e.g.f. exp(x/(x-1)).
%H A293116 Seiichi Manyama, <a href="/A293116/b293116.txt">Table of n, a(n) for n = 0..450</a>
%H A293116 Geoffrey B. Campbell, <a href="https://arxiv.org/abs/2309.16094">Visible Point Vector Partition Identities for Hyperpyramid Lattices</a>, arXiv:2309.16094 [math.CO], 2023. See pp. 14, 27.
%F A293116 E.g.f.: exp(x/(x-1)).
%F A293116 a(n) = (-1)^n * A111884(n).
%F A293116 E.g.f.: Product_{k>=1} (1 - x^k)^(phi(k)/k), where phi() is the Euler totient function (A000010). - _Ilya Gutkovskiy_, May 25 2019
%F A293116 D-finite with recurrence a(n) +(-2*n+3)*a(n-1) +(n-1)*(n-2)*a(n-2)=0. - _R. J. Mathar_, Mar 13 2023
%p A293116 a:= proc(n) option remember; `if`(n=0, 1, -add(
%p A293116 a(n-j)*binomial(n-1, j-1)*j!, j=1..n))
%p A293116 end:
%p A293116 seq(a(n), n=0..25); # _Alois P. Heinz_, Sep 30 2017
%t A293116 CoefficientList[Series[E^(-x/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2017 *)
%o A293116 (PARI) my(x='x+O('x^66)); Vec(serlaplace(exp(x/(x-1))))
%Y A293116 Column k=0 of A293119.
%Y A293116 Cf. A000262, A066668, A111884.
%K A293116 sign
%O A293116 0,6
%A A293116 _Seiichi Manyama_, Sep 30 2017