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Search: id:A052319
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| A052319 |
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Number of increasing rooted trimmed trees with n nodes. |
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+0
5
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| 1, 1, 1, 2, 7, 28, 131, 720, 4513, 31824, 249513, 2151744, 20242983, 206313024, 2264425179, 26628836352, 334022337153, 4451717814528, 62820790592913, 935750983412736, 14672143677452679, 241555066200437760
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
A trimmed tree is a tree with a forbidden limb of length 2.
A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps.
a(n)=number of permutations on [n+1] beginning with 12 and avoiding a consecutive 132 pattern (n>=1). For example, a(4)=2 counts 12345, 12453. - Ralf Stephan, Apr 25 2004
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LINKS
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S. Kitaev and T. Mansour, Simultaneous avoidance of generalized patterns.
Index entries for sequences related to rooted trees
S. Kitaev, Generalized pattern avoidance with additional restrictions, Sem. Lothar. Combinat. B48e (2003).
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FORMULA
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E.g.f.: A(x) = 1/B(-x) where B'(x) is e.g.f. of A006882 and B(0) = 1.
E.g.f. satisfies A'(x) = exp(A(x)-x^2/2).
E.g.f.: exp(-x^2/2)/(1-int[0..x, exp(-x^2/2)]). - Ralf Stephan, Apr 25 2004
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CROSSREFS
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Cf. A002955, A002988-A002992, A052318-A052329.
Sequence in context: A112565 A118926 A127084 this_sequence A127783 A116539 A141318
Adjacent sequences: A052316 A052317 A052318 this_sequence A052320 A052321 A052322
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KEYWORD
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nonn,eigen
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Dec 11 1999. Formula updated Mar 06, 2001.
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