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A002718
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Number of bicoverings of an n-set.
(Formerly M4559 N1941)
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36
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1, 8, 80, 1088, 19232, 424400, 11361786, 361058000, 13386003873, 570886397340, 27681861184474, 1511143062540976, 92091641176725504, 6219762391554815200, 462595509951068027741, 37676170944802047077248
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OFFSET
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2,2
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COMMENTS
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Another description: number of proper 2-covers of [1,...,n].
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REFERENCES
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Cameron, Peter; Prellberg, Thomas; and Stark, Dudley; Asymptotic enumeration of 2-covers and line graphs. Discrete Math. 310 (2010), no. 2, 230-240 (see t_n).
L. Comtet, Birecouvrements et birevetements d'un ensemble fini. Studia Sci. Math. Hungar. 3 1968 137-152.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #40.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=2..17.
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FORMULA
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E.g.f. for k-block bicoverings of an n-set is exp(-x-1/2*x^2*(exp(y)-1))*Sum_{i=0..inf} x^i/i!*exp(binomial(i, 2)*y).
Stirling_2 transform of A060053.
The e.g.f.'s of A002718 (T(x)) and A060053 (V(x)) are related by T(x) = V(e^x-1).
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MATHEMATICA
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nmax = 16; imax = 2*(nmax - 2); egf := E^(-x - 1/2*x^2*(E^y - 1))*Sum[(x^i/i!)*E^(Binomial[i, 2]*y), {i, 0, imax}]; fx = CoefficientList[Series[egf, {y, 0, imax}], y]*Range[0, imax]!; a[n_] := Drop[ CoefficientList[ Series[fx[[n + 1]], {x, 0, imax}], x], 3] // Total; Table[ a[n] , {n, 2, nmax}] (* Jean-François Alcover, Apr 04 2013 *)
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CROSSREFS
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Cf. A020554, A002719, A003462, A059945-A059951, A060053. Row sums of A059443.
Sequence in context: A051580 A060375 A097815 * A222825 A057707 A222671
Adjacent sequences: A002715 A002716 A002717 * A002719 A002720 A002721
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KEYWORD
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nonn,nice,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Vladeta Jovovic, Feb 18 2001
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STATUS
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approved
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