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 A373743 #10 Jun 16 2024 11:02:22
%S A373743 1,0,0,1,8,20,10,280,3360,20440,67200,462000,7407400,73673600,
%T A373743 482081600,3364761400,47311264000,657536880000,6586994814400,
%U A373743 58707179731200,740032028736000,11832726841936000,161121297104768000,1857897194273120000,23875495204536976000
%N A373743 Expansion of e.g.f. exp(x^3/6 * (1 + x)^2).
%F A373743 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(2*k,n-3*k)/(6^k * k!).
%F A373743 a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 8*(n-3)*a(n-4) + 5*(n-3)*(n-4)*a(n-5)).
%o A373743 (PARI) a(n) = n!*sum(k=0, n\3, binomial(2*k,n-3*k)/(6^k*k!));
%Y A373743 Cf. A361568, A372742.
%Y A373743 Cf. A361278, A361567.
%Y A373743 Cf. A264622.
%K A373743 nonn
%O A373743 0,5
%A A373743 _Seiichi Manyama_, Jun 16 2024