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 A078468 Distinct compositions of the complete graph with one edge removed (K^-_n). 0
 1, 4, 13, 47, 188, 825, 3937, 20270, 111835, 657423, 4097622, 26965867, 186685725, 1355314108, 10289242825, 81481911259, 671596664012, 5749877335253, 51042081429213, 469037073951694, 4454991580211951, 43677136038927595, 441452153556357966, 4594438326374915007 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS A. Knopfmacher and M. E. Mays, Graph Compositions. I: Basic Enumeration, Integers 1(2001), #A04. FORMULA a(n) = A000110(n+2)-A000110(n). E.g.f. (-1+exp(x)+exp(2*x))*exp(exp(x)-1). 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 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 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 EXAMPLE a(5) = A000110(7)-A000110(5) = 825. MAPLE with(combinat): a:=n->bell(n+2)-bell(n): seq(a(n), n=0..21); # Zerinvary Lajos, Jul 01 2007 CROSSREFS Cf. A000110. Sequence in context: A149440 A149441 A149442 * A149443 A125656 A279159 Adjacent sequences:  A078465 A078466 A078467 * A078469 A078470 A078471 KEYWORD nonn AUTHOR Ralf Stephan, Jan 02 2003 STATUS approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)