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 A293039 #21 Oct 19 2022 14:13:29
%S A293039 1,0,0,0,-1,-1,-1,-1,34,125,335,791,-4027,-41328,-223510,-966174,
%T A293039 -1082043,22493107,255137121,1853859145,8611832136,6734302429,
%U A293039 -364364045001,-4974309134233,-41550393316275,-223452696895652,-173393115915136,14282249293678744
%N A293039 E.g.f.: exp(1 + x + x^2/2! + x^3/3! - exp(x)).
%H A293039 Seiichi Manyama, <a href="/A293039/b293039.txt">Table of n, a(n) for n = 0..592</a>
%F A293039 a(0) = 1; a(n) = -Sum_{k=4..n} binomial(n-1,k-1) * a(n-k). - _Ilya Gutkovskiy_, Nov 20 2020
%t A293039 With[{nn=30},CoefficientList[Series[Exp[1+x+x^2/2!+x^3/3!-Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 19 2022 *)
%o A293039 (PARI) my(x='x+O('x^66)); Vec(serlaplace(exp(-exp(x)+1+x+x^2/2+x^3/6)))
%Y A293039 Column k=3 of A293051.
%Y A293039 Cf. A000587 (k=0), A293037 (k=1), A293038 (k=2), this sequence (k=3), A293040 (k=4).
%Y A293039 Cf. A057837.
%K A293039 sign
%O A293039 0,9
%A A293039 _Seiichi Manyama_, Sep 28 2017