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Search: id:A000248
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| A000248 |
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Number of forests with n nodes and height at most 1.
(Formerly M2857 N1148)
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+0
24
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| 1, 1, 3, 10, 41, 196, 1057, 6322, 41393, 293608, 2237921, 18210094, 157329097, 1436630092, 13810863809, 139305550066, 1469959371233, 16184586405328, 185504221191745, 2208841954063318, 27272621155678841
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equivalently, number of idempotent mappings f from a set of n elements into itself (i.e. satisfying f o f = f). - Robert FERREOL (ferreol(AT)mathcurve.com), Oct 11 2007
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91.
B. Harris and L. Schoenfeld, The number of idempotent elements in symmetric semigroups, J. Combin. Theory, 3 (1967), 122-135.
Nate Kube and Frank Ruskey, Sequences That Satisfy a(n-a(n))=0, Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.5.
J. Riordan, Forests of labeled trees, J. Combin. Theory, 5 (1968), 90-103.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.32(d).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 117
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FORMULA
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E.g.f.: exp(x*exp(x)).
G.f.: Sum_{k>=0} x^k/(1-k*x)^(k+1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 25 2003
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MAPLE
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A000248 := proc(n) local k; add(k^(n-k)*binomial(n, k).k=0..n); end; - Robert FERREOL (ferreol(AT)mathcurve.com), Oct 11 2007
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CROSSREFS
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First row of array A098697.
Sequence in context: A137781 A140046 A116540 this_sequence A030927 A002627 A030802
Adjacent sequences: A000245 A000246 A000247 this_sequence A000249 A000250 A000251
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KEYWORD
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easy,nonn,nice
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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