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 A357174 #12 Sep 16 2022 11:46:28
%S A357174 1,1,4,27,280,5045,134136,4269223,153188176,6657007113,371930499280,
%T A357174 25072409219891,1872319689314856,154583203638018493,
%U A357174 14784597239881491400,1641532369038107170815,201617558936011146124576,26755058016106471234608017
%N A357174 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^n/(n - 3*k)!.
%F A357174 E.g.f.: Sum_{k>=0} (k * x)^k / (k! * (1 - (k * x)^3)).
%t A357174 a[n_] := n! * Sum[(n - 3*k)^n/(n - 3*k)!, {k, 0, Floor[n/3]} ]; a[0] = 1; Array[a, 18, 0] (* _Amiram Eldar_, Sep 16 2022 *)
%o A357174 (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^n/(n-3*k)!);
%o A357174 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^k/(k!*(1-(k*x)^3)))))
%Y A357174 Cf. A256016, A356834.
%Y A357174 Cf. A353015, A357147.
%K A357174 nonn
%O A357174 0,3
%A A357174 _Seiichi Manyama_, Sep 16 2022