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A007852
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Antichains in rooted plane trees on n nodes.
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3
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1, 2, 7, 29, 131, 625, 3099, 15818, 82595, 439259, 2371632, 12967707, 71669167, 399751019, 2247488837, 12723799989, 72474333715, 415046380767, 2388355096446, 13803034008095
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Setting both offset to zero, this is the Catalan transform of A007317. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 29 2009]
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REFERENCES
| M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.
F. Ruskey, "Listing and Counting Subtrees of a Tree", SIAM J. Computing, 10 (1981) 141-150.
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LINKS
| Index entries for sequences related to rooted trees
Index entries for reversions of series
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FORMULA
| G.f.: A(z) = (1-B(z)-sqrt(1-5z-B(z)))/2, where B(z) = (1-sqrt(1-4z))/2.
a[ 1 ] = 1 and for n > 1 a[ n ] = sum( (a[ j ]+b[ j ])*a[ n-j ], j=1..n-1 ), where b[ n ] = C(2n-2, n-1)/n (Catalan number).
Also REVERT[A(x)] = x + 2*x^2 + x^3*(A007440(x) (Reversion of Fibonacci) - Olivier Gerard (olivier.gerard(AT)gmail.com), Jul 05 2001
a(n+1)=Sum_{k, 0<=k<=n}A039599(n,k)*A000108(k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 12 2007
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CROSSREFS
| Cf. A007440.
Sequence in context: A193040 A200755 A132262 * A110576 A074600 A064641
Adjacent sequences: A007849 A007850 A007851 * A007853 A007854 A007855
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KEYWORD
| nonn
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AUTHOR
| Martin Klazar (klazar(AT)kam.mff.cuni.cz)
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EXTENSIONS
| More terms and formulae from ruskey(AT)cs.uvic.ca (Frank Ruskey), Nov 15 1997
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