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 A366299 #5 Oct 08 2023 09:25:32
%S A366299 1,10,170,4300,145046,6115900,309453710,18267444100,1232400398966,
%T A366299 93535914320620,7887919177776350,731710341934820500,
%U A366299 74046493229735962886,8117679564133907097340,958393800813241073719790,121232569802975799394430500,16357741845227058108680934806,2345072789674603792983906178060
%N A366299 Expansion of e.g.f. 1 / (-3 + Sum_{k=1..4} exp(-k*x)).
%F A366299 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k) * (1 + 2^k + 3^k + 4^k) * a(n-k).
%t A366299 nmax = 17; CoefficientList[Series[1/(-3 + Sum[Exp[-k x], {k, 1, 4}]), {x, 0, nmax}], x] Range[0, nmax]!
%t A366299 a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k] (1 + 2^k + 3^k + 4^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]
%Y A366299 Cf. A001551, A004702, A005923, A319509, A366298, A366300, A366301, A366302.
%K A366299 nonn
%O A366299 0,2
%A A366299 _Ilya Gutkovskiy_, Oct 06 2023