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 A000424 M4448 N1883 #28 Apr 28 2020 11:50:32
%S A000424 7,85,1660,48076,1942416,104587344,7245893376,628308907776,
%T A000424 66687811660800,8506654697548800,1284292319599411200,
%U A000424 226530955276874956800,46165213716463676620800,10765453901922078105600000,2848453606917036402278400000,848800150518516674081587200000
%N A000424 Differences of reciprocals of unity.
%D A000424 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
%D A000424 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000424 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000424 Mircea Merca, <a href="https://www.researchgate.net/publication/264664262_Some_experiments_with_complete_and_elementary_symmetric_functions">Some experiments with complete and elementary symmetric functions</a>, Periodica Mathematica Hungarica, 69 (2014), 182-189.
%F A000424 From _Vaclav Kotesovec_, Oct 23 2017: (Start)
%F A000424 a(n) = (3*n^2 + 3*n + 1)*a(n-1) - 3*n^4*a(n-2) + (n-1)^3*n^3*a(n-3).
%F A000424 a(n) ~ Pi * log(n)^2 * n^(2*n + 3) * (1 + 2*gamma/log(n) + (gamma^2 + Pi^2/6) / log(n)^2) / exp(2*n), where gamma is the Euler-Mascheroni constant (A001620). (End)
%t A000424 T[n_, k_] := If[k <= n, (n-k+2)!^k*Sum[(-1)^(j+1)*Binomial[n-k+2, j]/j^k, {j, 1, n-k+2}], 0]; a[n_] := T[n+1, 2]; Table[a[n], {n, 1, 10}] (* _Jean-François Alcover_, Feb 08 2016, after _Alois P. Heinz_ in A008969 *)
%Y A000424 Essentially the same as A060237.
%Y A000424 Column 2 in triangle A008969.
%K A000424 nonn
%O A000424 1,1
%A A000424 _N. J. A. Sloane_
%E A000424 More terms from _Vaclav Kotesovec_, Oct 23 2017