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 A356633 #11 Aug 19 2022 09:25:51
%S A356633 1,1,2,6,28,160,1080,8540,78400,816480,9492000,122337600,1736380800,
%T A356633 26930904000,453515462400,8254694448000,161734564992000,
%U A356633 3397235761920000,76228261933824000,1821644243362944000,46233794313907200000,1242946827521118720000
%N A356633 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/6^k.
%F A356633 E.g.f.: Sum_{k>=0} x^k / (1 - k*x^3/6).
%t A356633 a[n_] := n! * Sum[(n - 3*k)^k/6^k, {k, 0, Floor[n/3]}]; a[0] = 1; Array[a, 22, 0] (* _Amiram Eldar_, Aug 19 2022 *)
%o A356633 (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/6^k);
%o A356633 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^3/6))))
%Y A356633 Cf. A356632, A356634.
%Y A356633 Cf. A352946.
%K A356633 nonn
%O A356633 0,3
%A A356633 _Seiichi Manyama_, Aug 18 2022