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 A367744 #6 Nov 29 2023 11:37:23
%S A367744 1,-4,7,17,-14,-637,-2951,14126,333205,2076245,-12283700,-423234511,
%T A367744 -4163106203,8148184700,952894223755,15568620884189,69314620864450,
%U A367744 -2816256959131561,-83397946135434515,-1025683419252783946,4726361848234575553,525779836596438636689,12363747028673287330948,112888493670408785796989
%N A367744 Expansion of e.g.f. exp(1 - x - exp(3*x)).
%F A367744 a(n) = exp(1) * Sum_{k>=0} (-1)^k * (3*k-1)^n / k!.
%F A367744 a(0) = 1; a(n) = -a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * 3^k * a(n-k).
%F A367744 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 3^k * A000587(k).
%t A367744 nmax = 23; CoefficientList[Series[Exp[1 - x - Exp[3 x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A367744 a[0] = 1; a[n_] := a[n] = -a[n - 1] - Sum[Binomial[n - 1, k - 1] 3^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
%t A367744 Table[Sum[(-1)^(n - k) Binomial[n, k] 3^k BellB[k, -1], {k, 0, n}], {n, 0, 23}]
%Y A367744 Cf. A000587, A004212, A109747, A284859, A284860, A317996, A367743.
%K A367744 sign
%O A367744 0,2
%A A367744 _Ilya Gutkovskiy_, Nov 29 2023