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A001862
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Number of forests of least height with n nodes.
(Formerly M1773 N0702)
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6
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1, 1, 2, 7, 26, 111, 562, 3151, 19252, 128449, 925226, 7125009, 58399156, 507222535, 4647051970, 44747776651, 451520086208, 4761032807937, 52332895618066, 598351410294193, 7102331902602676, 87365859333294151, 1111941946738682522, 14621347433458883187
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OFFSET
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0,3
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COMMENTS
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Also the number of minimal loop-graphs covering n vertices. This is the minimal case of A322661. For example, the a(0) = 1 through a(3) = 7 loop-graphs are (loops represented as singletons):
{} {1} {12} {1-23}
{1-2} {2-13}
{3-12}
{12-13}
{12-23}
{13-23}
{1-2-3}
(End)
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983. See (3.3.7): number of ways to cover the complete graph K_n with star graphs.
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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FORMULA
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E.g.f.: exp(x*(exp(x)-x/2)).
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MATHEMATICA
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Range[0, 20]! CoefficientList[Series[Exp[x Exp[x] - x^2/2], {x, 0, 20}], x] (* Geoffrey Critzer, Mar 13 2011 *)
fasmin[y_]:=Complement[y, Union@@Table[Union[s, #]& /@ Rest[Subsets[Complement[Union@@y, s]]], {s, y}]];
Table[Length@fasmin[Select[Subsets[Subsets[Range[n], {1, 2}]], Union@@#==Range[n]&]], {n, 0, 4}] (* Gus Wiseman, Feb 14 2024 *)
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CROSSREFS
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This is the minimal case of A322661.
A006125 counts simple graphs; also loop-graphs if shifted left.
A054548 counts graphs covering n vertices with k edges, with loops A369199.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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