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 A361595 #10 Mar 17 2023 08:25:50
%S A361595 1,1,2,12,120,1320,15480,199080,2862720,46146240,826156800,
%T A361595 16212873600,344741443200,7875365097600,192137321376000,
%U A361595 4984375210214400,136994756496998400,3976455027389644800,121533921410994892800,3900447928934548992000
%N A361595 Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x).
%F A361595 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n,3*k)/k!.
%F A361595 From _Vaclav Kotesovec_, Mar 17 2023: (Start)
%F A361595 a(n) = (4*n - 3)*a(n-1) - 3*(n-1)*(2*n - 3)*a(n-2) + 2*(n-2)*(n-1)*(2*n - 3)*a(n-3) - (n-3)^2*(n-2)*(n-1)*a(n-4).
%F A361595 a(n) ~ 3^(-1/8) * exp(-1/4 + 5*3^(-1/4)*n^(1/4)/8 - sqrt(3*n)/2 + 4*3^(-3/4) * n^(3/4) - n) * n^(n + 1/8) / 2 * (1 + (1511/2560)*3^(1/4)/n^(1/4)). (End)
%t A361595 Table[n! * Sum[Binomial[n,3*k]/k!, {k,0,n/3}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 17 2023 *)
%o A361595 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^3)/(1-x)))
%Y A361595 Cf. A002720, A361594.
%Y A361595 Cf. A361572.
%K A361595 nonn
%O A361595 0,3
%A A361595 _Seiichi Manyama_, Mar 16 2023