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 A001338 M1759 N0697 #27 Dec 24 2014 23:02:06
%S A001338 1,0,2,7,23,88,414,2371,16071,125672,1112082,10976183,119481295,
%T A001338 1421542640,18348340126,255323504931,3809950977007,60683990530224,
%U A001338 1027542662934914,18430998766219335,349096664728623335,6962409983976703336,145841989688186383358
%N A001338 -1 + Sum (k-1)! C(n,k), k = 1..n for n > 0, a(0) = 1.
%D A001338 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001338 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001338 T. D. Noe, <a href="/A001338/b001338.txt">Table of n, a(n) for n = 0..100</a>
%H A001338 E. Biondi, L. Divieti, G. Guardabassi, <a href="http://dx.doi.org/10.4153/CJM-1970-003-9">Counting paths, circuits, chains and cycles in graphs: A unified approach</a>, Canad. J. Math. 22 1970 22-35.
%F A001338 Conjecture: a(n) +(-n-1)*a(n-1) +2*(n-1)*a(n-2) +(-n+2)*a(n-3)=0. - _R. J. Mathar_, Feb 16 2014
%F A001338 a(n) = n*a(n-1) - (n-1)*a(n-2) - 1, with a sign reversal for n>=2. - _Richard R. Forberg_, Dec 16 2014
%t A001338 Join[{1}, Table[-1 + Sum[(k - 1)! Binomial[n, k], {k, n}], {n, 20}]] (* _T. D. Noe_, Jun 28 2012 *)
%Y A001338 Partial sums of A000522.
%Y A001338 Equals A002104(n) + 1.
%K A001338 nonn
%O A001338 0,3
%A A001338 _N. J. A. Sloane_