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 A375227 #12 Jul 04 2025 13:48:46
%S A375227 1,3,12,66,504,5040,60840,839160,12882240,217607040,4018896000,
%T A375227 80691811200,1750850640000,40809559190400,1016150162227200,
%U A375227 26898872647046400,753882642267955200,22291971504503500800,693356807039126630400
%N A375227 Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x)^3.
%F A375227 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n+2,n-3*k)/k!.
%t A375227 With[{nn=20},CoefficientList[Series[Exp[(x/(1-x))^3]/(1-x)^3,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 04 2025 *)
%o A375227 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^3)/(1-x)^3))
%o A375227 (PARI) a(n) = n!*sum(k=0, n\3, binomial(n+2, n-3*k)/k!);
%Y A375227 Cf. A361595, A375226.
%K A375227 nonn
%O A375227 0,2
%A A375227 _Seiichi Manyama_, Aug 06 2024