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Search: id:A007857
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| A007857 |
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Number of independent sets in rooted plane trees on n nodes. |
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+0
5
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| 1, 2, 8, 37, 184, 959, 5172, 28641, 162008, 932503, 5445934, 32197334, 192357788, 1159603592, 7045356104, 43098733353, 265240985112, 1641100253735, 10202295895890, 63696629668980, 399216722146770, 2510833297584165
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals the main diagonal of square array A130523. - Paul D. Hanna (pauldhanna(AT)juno.com), Jun 06 2007
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REFERENCES
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M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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a(n)=(2/(n+1))*C(3n,n)-(1/(n+1))*C(2n,n); a(n)=A007226(n)-A000108(n); - Paul Barry (pbarry(AT)wit.ie), Nov 05 2006
G.f.: A(x) = x/[1 - xC(x)F(x) - xF(x)^2] where C(x) is g.f. of Catalan numbers (A000108): C(x) = 1 + xC(x)^2 and F(x) is g.f. of ternary numbers (A001764): F(x) = 1 + xF(x)^3. - Paul D. Hanna (pauldhanna(AT)juno.com), Jun 06 2007
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PROGRAM
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(PARI) {a(n)=local(A000108, A001764); A000108=Ser(vector(n+1, r, binomial(2*r-2, r-1)/r)); A001764=Ser(vector(n+1, r, binomial(3*r-3, r-1)/(2*r-1))); polcoeff(x/(1-x*A000108*A001764-x*A001764^2 +x*O(x^n)), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jun 06 2007
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CROSSREFS
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Cf. A000108, A001764; A130523.
Sequence in context: A052618 A055142 A046814 this_sequence A047729 A020076 A020130
Adjacent sequences: A007854 A007855 A007856 this_sequence A007858 A007859 A007860
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KEYWORD
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nonn
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AUTHOR
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Martin Klazar (klazar(AT)kam.mff.cuni.cz)
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EXTENSIONS
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More terms from Paul Barry (pbarry(AT)wit.ie), Nov 05 2006
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