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 A078468 #34 Aug 17 2021 19:30:37
%S A078468 1,4,13,47,188,825,3937,20270,111835,657423,4097622,26965867,
%T A078468 186685725,1355314108,10289242825,81481911259,671596664012,
%U A078468 5749877335253,51042081429213,469037073951694,4454991580211951,43677136038927595,441452153556357966,4594438326374915007
%N A078468 Distinct compositions of the complete graph with one edge removed (K^-_n).
%H A078468 A. Knopfmacher and M. E. Mays, <a href="http://www.emis.de/journals/INTEGERS/papers/b4/b4.Abstract.html">Graph Compositions. I: Basic Enumeration</a>, Integers 1(2001), #A04.
%F A078468 a(n) = A000110(n+2) - A000110(n).
%F A078468 E.g.f.: (-1+exp(x)+exp(2*x))*exp(exp(x)-1).
%F A078468 G.f.: (G(0)*(1-x)-1-x)/x^2 where G(k) = 1 - 2*x*(k+1)/((2*k+1)*(2*x*k-1) - x*(2*k+1)*(2*k+3)*(2*x*k-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+x-1)/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Jan 03 2013
%F A078468 G.f.: - G(0)*(1+1/x) where G(k) = 1 - 1/(1-x*(k+1))/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Feb 07 2013
%F A078468 G.f.: (Q(0) -1)*(1+x)/x^2, where Q(k) = 1 - x^2*(k+1)/( x^2*(k+1) - (1-x*(k+1))*(1-x*(k+2))/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Oct 10 2013
%F A078468 a(n) = Sum_{k=0..n} Stirling2(n,k) * (k+1)^2. - _Ilya Gutkovskiy_, Aug 09 2021
%e A078468 a(5) = A000110(7)-A000110(5) = 825.
%p A078468 with(combinat): a:=n->bell(n+2)-bell(n): seq(a(n), n=0..21); # _Zerinvary Lajos_, Jul 01 2007
%Y A078468 Cf. A000110, A033452.
%K A078468 nonn
%O A078468 0,2
%A A078468 _Ralf Stephan_, Jan 02 2003