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A132891
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Sum of the heights of all left factors of Dyck paths of length n.
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1
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1, 3, 6, 14, 28, 61, 121, 257, 508, 1065, 2103, 4372, 8634, 17842, 35254, 72524, 143396, 293968, 581630, 1189102, 2354168, 4802331, 9512984, 19370764, 38391332, 78056544, 154773135, 314281350, 623427154, 1264546021
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| See A132890 for the statistic "height" on left factors of Dyck paths.
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FORMULA
| a(n)=Sum(k*A132890(n,k),k=1..n).
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EXAMPLE
| a(4)=14 because the six left factors of Dyck paths of length 4 are UDUD, UDUU, UUDD, UUDU, UUUD and UUUU, having heights 1, 2, 2, 2, 3 and 4, respectively.
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MAPLE
| v := ((1-sqrt(1-4*z^2))*1/2)/z: g := proc (k) options operator, arrow: v^k*(1+v)*(1+v^2)/((1+v^(k+1))*(1+v^(k+2))) end proc: T := proc (n, k) options operator, arrow; coeff(series(g(k), z = 0, 70), z, n) end proc: seq(add(k*T(n, k), k = 1 .. n), n = 1 .. 30);
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CROSSREFS
| Cf. A132890.
Sequence in context: A030012 A001970 A006951 * A200544 A055890 A038359
Adjacent sequences: A132888 A132889 A132890 * A132892 A132893 A132894
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 08 2007
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