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 A084915 #17 May 07 2019 08:36:23
%S A084915 0,1,8,108,2304,72000,3110400,177811200,13005619200,1185137049600,
%T A084915 131681894400000,17526860144640000,2753310393630720000,
%U A084915 504085244567224320000
%N A084915 a(n) = (n!)^2*n.
%C A084915 Used to prove that Sum_{n>=1} 1/A002378(n) = 1. Examining Sum_{n=1..k} 1/A002378(n) gives 1/2, 1/2 + 1/6, 1/2 + 1/6 + 1/12. Simplifying gives 1/2, 8/12, 108/144, where the numerators are this sequence and the denominators are A010790. Therefore we have k!^2*k/k!(k+1)! = k*k!/(k+1)! = k/(k+1), which tends to 1 as k tends to infinity.
%F A084915 a(n) = n!*(n+1)! - n!^2.
%F A084915 a(n) = det(PS(i+2,j+1), 1 <= i,j <= n-1), where PS(n,k) are Legendre-Stirling numbers of the second kind (A071951) and n > 0. [_Mircea Merca_, Apr 06 2013]
%e A084915 a(3) = 3!^2*3 = 36*3 = 108.
%o A084915 (PARI) for(n=1,50,print1(n!^2*n","))
%Y A084915 Cf. A002378, A010790, A071951.
%K A084915 nonn
%O A084915 0,3
%A A084915 _Jon Perry_, Jul 14 2003