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A078468
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Distinct compositions of the complete graph with one vertex removed (K^-_n).
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0
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1, 4, 13, 47, 188, 825, 3937, 20270, 111835, 657423, 4097622, 26965867, 186685725, 1355314108, 10289242825, 81481911259, 671596664012, 5749877335253, 51042081429213, 469037073951694, 4454991580211951, 43677136038927595
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..21.
A. Knopfmacher and M.E. Mays, Graph compositions,Integers 1(2001), #A04.
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FORMULA
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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
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EXAMPLE
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a(5)=A000110(7)-A000110(5)=825.
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MAPLE
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with (combinat):a:=n->bell(n+2)-bell(n): seq(a(n), n=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 01 2007
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CROSSREFS
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Cf. A000110.
Sequence in context: A149440 A149441 A149442 * A149443 A125656 A149444
Adjacent sequences: A078465 A078466 A078467 * A078469 A078470 A078471
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Jan 02 2003
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STATUS
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approved
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