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 A356328 #23 Aug 19 2022 09:19:21
%S A356328 1,1,1,1,5,21,61,281,2521,15625,84841,971521,10646461,83366141,
%T A356328 962405445,15445935961,181502928881,2182235585041,42297481449361,
%U A356328 714940186390465,10007476059187381,204722588272279141,4600003555996715021,80767827313930590681
%N A356328 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * (n - 3*k)!).
%F A356328 E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^3/6)).
%t A356328 a[n_] := n! * Sum[(n - 3*k)^k/(6^k*(n - 3*k)!), {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 24, 0] (* _Amiram Eldar_, Aug 19 2022 *)
%o A356328 (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*(n-3*k)!));
%o A356328 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^3/6)))))
%Y A356328 Cf. A354436, A356029, A356608.
%Y A356328 Cf. A354551, A356629, A356633.
%K A356328 nonn
%O A356328 0,5
%A A356328 _Seiichi Manyama_, Aug 18 2022