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Search: id:A091135
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| A091135 |
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Number of Dyck paths of semilength n+4, having exactly two long ascents (i.e. ascents of length at least two). |
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+0
1
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| 2, 15, 69, 252, 804, 2349, 6455, 16962, 43086, 106587, 258153, 614520, 1441928, 3342489, 7667883, 17432766, 39321810, 88080615, 196083965, 434110740, 956301612, 2097152325, 4580180319, 9965666682, 21609054614, 46707769779
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Also number of ordered trees with n+4 edges, having exactly two branch nodes (i.e. vertices of outdegree at least two).
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FORMULA
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a(n)=(n^2+9n+20)/2+2^(n+1)*(n^2+3n-4). G.f.=(2-3z)/[(1-2z)^3*(1-z)^3].
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EXAMPLE
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a(0)=2 because the only Dyck paths of semilength 4 that have exactly two long ascents are UUDDUUDD and UUDUUDDD (here U=(1,1) and D=(1,-1)).
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CROSSREFS
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Cf. A000108.
Sequence in context: A117669 A117393 A055206 this_sequence A056037 A125903 A007232
Adjacent sequences: A091132 A091133 A091134 this_sequence A091136 A091137 A091138
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2004
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