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 A367819 #9 Dec 02 2023 07:49:28
%S A367819 1,-5,24,-111,497,-2166,9239,-38765,160658,-659773,2691205,-10922544,
%T A367819 44166173,-178098121,716703848,-2879774019,11558005677,-46348854134,
%U A367819 185746261419,-744036460097,2979305960426,-11926715433881,47735079979633,-191026723545976,764362047956073,-3058170811731677
%N A367819 Expansion of e.g.f. exp(1 - 4*x - exp(x)).
%F A367819 G.f. A(x) satisfies: A(x) = 1 - 4*x*A(x) - x * A(x/(1 - x)) / (1 - x).
%F A367819 a(n) = exp(1) * Sum_{k>=0} (-1)^k * (k-4)^n / k!.
%F A367819 a(0) = 1; a(n) = -4*a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * a(n-k).
%F A367819 a(n) = Sum_{k=0..n} binomial(n,k) * (-4)^(n-k) * A000587(k).
%t A367819 nmax = 25; CoefficientList[Series[Exp[1 - 4 x - Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A367819 a[0] = 1; a[n_] := a[n] = -4 a[n - 1] - Sum[Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]
%t A367819 Table[Sum[Binomial[n, k] (-4)^(n - k) BellB[k, -1], {k, 0, n}], {n, 0, 25}]
%o A367819 (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(1 - 4*x - exp(x)))) \\ _Michel Marcus_, Dec 02 2023
%Y A367819 Cf. A000587, A045379, A109747, A153732, A193684, A346739, A367818.
%K A367819 sign
%O A367819 0,2
%A A367819 _Ilya Gutkovskiy_, Dec 01 2023