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 A282010 Number of ways to partition Turan graph T(2n,n) into connected components. 1
 1, 1, 12, 163, 3411, 97164, 3576001, 163701521, 9064712524, 594288068019, 45352945127123, 3973596101084108, 395147058261233761, 44170986458602383553, 5504694207040057913164, 759355292729159336345955, 115228949414563130433140659, 19129024114529146183236435660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Turan graph T(2n,n) is also called cocktail party graph, so a(n) is the number of ways to seat n married couples for one or a few tables in such a manner that no table is fully occupied by any couple. If we dissect (n-1)-skeleton of n-cube along some (n-2)-edges into some parts, then a(n) is the number of ways of such dissections. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..100 Eric Weisstein's World of Mathematics, Cocktail Party Graph Eric Weisstein's World of Mathematics, Turan Graph FORMULA a(n) = Sum_{j=0..n} ((-1)^(n-j))*A020557(j)*binomial(n,j). a(n) = Sum_{j=0..n} ((-1)^(n-j))*A000110(2*j)*binomial(n,j). EXAMPLE For n=1, Turan graph T(2,1) (2-empty graph) shall be partitioned into two singleton subgraphs (1 way), a(1)=1. For n=2, Turan graph T(4,2) (square graph) shall be partitioned into: the same square graph (1 way) or one singleton + one 3-path subgraphs (4 ways) or two singleton + one 2-path subgraphs (4 ways) or two 2-path subgraphs (2 ways) or four singleton subgraphs (1 way), a(2)=12. MATHEMATICA a[n_]:=BellB[2n]; Table[Sum[((-1)^(n-j))*a[j]*Binomial[n, j], {j, 0, n}], {n, 0, 17}] (* Indranil Ghosh, Feb 25 2017 *) PROG (PARI) bell(n) = polcoeff( sum( k=0, n, prod(i=1, k, x/(1 - i*x)), x^n * O(x)), n) a(n) = sum(j=0, n, ((-1)^(n-j))*bell(2*j)*binomial(n, j)); \\ Michel Marcus, Feb 05 2017 CROSSREFS Cf. A000110, A020557 Sequence in context: A138455 A024221 A093152 * A143583 A231541 A203372 Adjacent sequences:  A282007 A282008 A282009 * A282011 A282012 A282013 KEYWORD nonn,easy AUTHOR Tengiz Gogoberidze, Feb 04 2017 EXTENSIONS More terms from Michel Marcus, Feb 05 2017 STATUS approved

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Last modified September 26 12:17 EDT 2022. Contains 356997 sequences. (Running on oeis4.)