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 A111420 #8 May 11 2020 15:21:36
%S A111420 0,1,19,315,6601,178923,6161065,262268499,13470911521,818285112123,
%T A111420 57836073876505,4693152951066099,432360761046527041,
%U A111420 44794795435021490043,5176959026638375267225,662704551819559746282579,93384393940399990403502241,14406589076081640590750974203
%N A111420 a(n) = Sum_{q=0..n} Stirling2(n+1,q)^2*q!.
%p A111420 a:= n-> add(Stirling2(n+1,q)^2*q!, q=0..n):
%p A111420 seq(a(n), n=0..19); # _Alois P. Heinz_, May 11 2020
%t A111420 Table[Sum[StirlingS2[n+1, k]^2 * k!, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 12 2018 *)
%Y A111420 Cf. A023997, A014235.
%K A111420 nonn
%O A111420 0,3
%A A111420 _N. J. A. Sloane_, Nov 14 2005