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 A373773 #10 Jun 18 2024 10:01:30
%S A373773 1,1,2,7,36,240,1930,17990,189840,2233000,28949200,410009600,
%T A373773 6297999400,104275571400,1851050401200,35065930299400,705993054166400,
%U A373773 15051593241484800,338705933426660800,8021585392026606400,199416162740963168000,5191567315003621552000
%N A373773 Expansion of e.g.f. exp(x^3 / (6 * (1 - x)^2)) / (1 - x).
%F A373773 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-k,n-3*k)/(6^k * k!).
%F A373773 From _Vaclav Kotesovec_, Jun 18 2024: (Start)
%F A373773 Recurrence: 6*a(n) = 6*(3*n-2)*a(n-1) - 6*(n-1)*(3*n-4)*a(n-2) + 3*(n-2)*(n-1)*(2*n-3)*a(n-3) - (n-3)*(n-2)*(n-1)*a(n-4).
%F A373773 a(n) ~ 3^(-1/3) * exp(19/72 - 3^(-2/3)*n^(1/3) + 3^(2/3)*n^(2/3)/2 - n) * n^(n + 1/6). (End)
%o A373773 (PARI) a(n) = n!*sum(k=0, n\3, binomial(n-k, n-3*k)/(6^k*k!));
%Y A373773 Cf. A130906, A361597, A373772.
%Y A373773 Cf. A361596, A361598.
%Y A373773 Cf. A373757.
%K A373773 nonn
%O A373773 0,3
%A A373773 _Seiichi Manyama_, Jun 18 2024