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A125107
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Subtract compositions (A011782) from Catalan numbers (A000108).
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2
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0, 0, 0, 1, 6, 26, 100, 365, 1302, 4606, 16284, 57762, 205964, 738804, 2666248, 9678461, 35324902, 129579254, 477507628, 1767001046, 6563596132, 24465218444, 91480466488, 343055419346, 1289895758716, 4861929624236, 18367319517720
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OFFSET
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0,5
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COMMENTS
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Apparently the number of Dyck n-paths with more than half of the path lying between the first and last peaks. - David Scambler, Sep 14 2012
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LINKS
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Table of n, a(n) for n=0..26.
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FORMULA
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a(n) = A000108(n) - A011782(n).
Conjecture: (n+1)*a(n) +2*(1-4*n)*a(n-1) +4*(5*n-7)*a(n-2) +8*(5-2*n)*a(n-3)=0. - R. J. Mathar, Aug 10 2013
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EXAMPLE
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A000108 begins 1 1 2 5 14 42 132 429 ...
A011782 begins 1 1 2 4 8 16 32 64 ...
so we get .... 0 0 0 1 6 26 100 365 ...
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MATHEMATICA
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Table[CatalanNumber[n] - If[n==0, 1, 2^(n-1)], {n, 0, 30}] (* David Scambler, Sep 14 2012 *)
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CROSSREFS
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Cf. A000079, A000108, A000110, A011782, A016098.
Sequence in context: A261064 A094811 A005022 * A301476 A290347 A034560
Adjacent sequences: A125104 A125105 A125106 * A125108 A125109 A125110
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KEYWORD
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easy,nonn
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AUTHOR
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Alford Arnold, Dec 15 2006
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EXTENSIONS
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More terms from David Scambler, Sep 14 2012
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STATUS
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approved
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