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 A373742 #8 Jun 16 2024 11:02:18
%S A373742 1,0,0,1,4,0,10,140,560,280,8400,92400,385000,800800,16816800,
%T A373742 169569400,784784000,3811808000,68803134400,673546473600,
%U A373742 3693641952000,30454440016000,507477434464000,5002277568288000,33870732912016000,386622918281600000
%N A373742 Expansion of e.g.f. exp(x^3/6 * (1 + x)).
%F A373742 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(k,n-3*k)/(6^k * k!).
%F A373742 a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 4*(n-3)*a(n-4)).
%o A373742 (PARI) a(n) = n!*sum(k=0, n\3, binomial(k, n-3*k)/(6^k*k!));
%Y A373742 Cf. A361568, A372743.
%Y A373742 Cf. A017817.
%K A373742 nonn
%O A373742 0,5
%A A373742 _Seiichi Manyama_, Jun 16 2024