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 A190194 #13 Dec 29 2017 17:44:28
%S A190194 0,1,4,20,116,776,5912,50648,482552,5065016,58099832,723315128,
%T A190194 9715154552,140051879096,2157103991672,35355232693688,614453167841912,
%U A190194 11287370521073336,218535622980161912,4447889360078673848,94944254697268017272,2120984032794061422776,49489160848954807154552,1203943675008917425902008,30486416629523244528307832
%N A190194 a(n) = Sum_{r=0..n-1} Sum_{s=r+1..n} s! * r^(n-s).
%C A190194 The expression a(n)/n! = A190186/A190187 arises in the analysis of bubble sort [Knuth].
%D A190194 D. E. Knuth, The Art of Computer Programming, Vol. 3, Section 5.2.2, p. 129.
%H A190194 G. C. Greubel, <a href="/A190194/b190194.txt">Table of n, a(n) for n = 0..445</a>
%p A190194 f:=proc(n) local t1,r,s;
%p A190194 t1:=add( add(s!*r^(n-s), s=r+1..n), r=0..n-1);
%p A190194 end;
%t A190194 Join[{0}, Table[Sum[n! + Sum[s!*k^(n - s), {s, k + 1, n - 1}], {k, 0, n - 1}], {n, 1, 50}]] (* _G. C. Greubel_, Dec 28 2017 *)
%o A190194 (PARI) for(n=0,30, print1(if(n==0,0, sum(k=0,n-1, n! + sum(s=k+1,n-1, s!*k^(n-s)))), ", ")) \\ _G. C. Greubel_, Dec 28 2017
%Y A190194 Cf. A190186, A190187.
%K A190194 nonn
%O A190194 0,3
%A A190194 _N. J. A. Sloane_, May 05 2011