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 A258845 #12 Mar 24 2017 13:47:41
%S A258845 0,0,1,7,52,332,2832,22704,242112,2662848,30620160,354965760,
%T A258845 5057925120,68627036160,1054183818240,17469144806400,321351896678400,
%U A258845 5609441772748800,112707637036646400,2192664093342105600,47745925079924736000,1065919878891012096000
%N A258845 The pi-based arithmetic derivative of n!.
%H A258845 Alois P. Heinz, <a href="/A258845/b258845.txt">Table of n, a(n) for n = 0..450</a>
%F A258845 a(n) = A258851(n!) = A258851(A000142(n)).
%p A258845 with(numtheory):
%p A258845 d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]):
%p A258845 a:= proc(n) option remember;
%p A258845 `if`(n<2, 0, a(n-1)*n+(n-1)!*d(n))
%p A258845 end:
%p A258845 seq(a(n), n=0..25);
%t A258845 d[n_] := n*Sum[i[[2]]*PrimePi[i[[1]]]/i[[1]], {i, FactorInteger[n]}];
%t A258845 a[n_] := a[n] = If[n < 2, 0, a[n-1]*n + (n-1)!*d[n]];
%t A258845 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Mar 24 2017, translated from Maple *)
%Y A258845 Cf. A000142, A000720, A258851, A259409.
%K A258845 nonn
%O A258845 0,4
%A A258845 _Alois P. Heinz_, Jun 12 2015