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A346158
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Total number of weak left-to-right maxima in Dyck paths of semilength n.
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2
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0, 1, 3, 9, 29, 98, 341, 1210, 4356, 15860, 58276, 215748, 803779, 3010514, 11327360, 42789497, 162200621, 616735888, 2351425517, 8987222524, 34425268864, 132128622038, 508050009119, 1956763431726, 7548022312030, 29156726321546, 112773951773678, 436719024636650
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{r=1..n} (d(r+2)-d(r))*(binomial(2*n-1,n-r)-binomial(2*n-1, n-r-1)) where d is A000005 and binomial is A007318.
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MAPLE
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a:= n-> (d-> add((binomial(2*n-1, n-r)-binomial(2*n-1, n-r-1))
*(d(r+2)-d(r)), r=1..n))(numtheory[tau]):
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PROG
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(PARI) a(n) = sum(r=1, n, (numdiv(r+2)-numdiv(r))*(binomial(2*n-1, n-r)-binomial(2*n-1, n-r-1)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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