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 A368854 #9 Jan 08 2024 09:00:55
%S A368854 1,5,121,7259,871081,182927009,61463475025,30977591412599,
%T A368854 22303865817071281,22080827158900568189,29146691849748750009481,
%U A368854 50015723214168855016269395,109234339499744779355532358681,298209746834303247640603339199129
%N A368854 a(n) = n! * (n+1)! * (n+2)! * Sum_{k=0..n} (-1)^k/(k! * (k+1)! * (k+2)!).
%F A368854 a(n) = n * (n+1) * (n+2) * a(n-1) + (-1)^n.
%F A368854 a(n) ~ c * n!*(n+1)!*(n+2)!, where c = hypergeom([], [2, 3], -1)/2 = 0.42008149848198278018826635149001977031641229888902795699817... - _Vaclav Kotesovec_, Jan 08 2024
%o A368854 (PARI) a(n) = n!*(n+1)!*(n+2)!*sum(k=0, n, (-1)^k/(k!*(k+1)!*(k+2)!));
%Y A368854 Cf. A000166, A368853.
%Y A368854 Cf. A368839.
%K A368854 nonn,easy
%O A368854 0,2
%A A368854 _Seiichi Manyama_, Jan 07 2024