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 A348597 #13 Apr 05 2022 17:08:48
%S A348597 1,1,2,5,20,100,601,4207,33656,302903,3029030,33319330,399831961,
%T A348597 5197815493,72769416902,1091541253529,17464660056464,296899220959888,
%U A348597 5344185977277985,101539533568281715,2030790671365634300,42646604098678320299,938225290170923046578
%N A348597 a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (3*k)!.
%F A348597 E.g.f.: (exp(-x) + 2 * exp(x/2) * cos(sqrt(3)*x/2)) / (3*(1 - x)).
%F A348597 a(n) = round(c * n!), where c = 0.834719468... = A346441.
%t A348597 Table[n! Sum[(-1)^k/(3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
%t A348597 nmax = 22; CoefficientList[Series[(Exp[-x] + 2 Exp[x/2] Cos[Sqrt[3] x/2])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
%Y A348597 Cf. A000166, A009102, A346441, A349087, A352659.
%K A348597 nonn
%O A348597 0,3
%A A348597 _Ilya Gutkovskiy_, Mar 25 2022