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Search: id:A112308
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| A112308 |
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Sum of the heights of the second peaks in all Dyck paths of semilength n+2. |
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+0
2
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| 1, 6, 25, 93, 333, 1180, 4183, 14895, 53349, 192239, 696765, 2539157, 9299547, 34215102, 126411177, 468822297, 1744799967, 6514363557, 24393558687, 91591471287, 344764147407, 1300756937445, 4918188617379, 18633066901747
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=sum(k*A112307(n+2,k), k=0..n+1).
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FORMULA
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G.f.=c^4*(1+zc)/(1-z), where c=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
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a(1)=6 because the second peaks of the Dyck paths UDUDUD, UDUUDD, UUDDUD, UUDUDD and UUUDDD, where U=(1,1), D=(1,-1), are 1, 2, 1, 2 and 0, respectively.
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MAPLE
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c:=(1-sqrt(1-4*z))/2/z: g:=series(c^4*(1+z*c)/(1-z), z=0, 32): 1, seq(coeff(g, z^n), n=1..27);
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CROSSREFS
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Cf. A112307.
Sequence in context: A099948 A143815 A092491 this_sequence A034336 A092184 A034559
Adjacent sequences: A112305 A112306 A112307 this_sequence A112309 A112310 A112311
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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), Nov 30 2005
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