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A293962
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Number of linear chord diagrams having n chords and maximal chord length n, a(0)=1.
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2
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1, 1, 2, 10, 70, 630, 6930, 90090, 1351350, 22972950, 436486050, 9166207050, 210822762150, 5270569053750, 142305364451250, 4126855569086250, 127932522641673750, 4221773247175233750, 147762063651133181250, 5467196355091927706250, 213220657848585180543750
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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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E.g.f.: (x + 1 + 2/sqrt(1-2*x))/3.
a(n) = (2*n-1)*a(n-1) for n > 2, a(0) = a(1) = 1, a(2) = 2.
a(n) = 2/3 * A001147(n) = 2/3 * (2n-1)!! for n>1.
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MAPLE
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a:= proc(n) option remember; `if`(n<3, [1, 1, 2][n+1],
(2*n-1)*a(n-1))
end:
seq(a(n), n=0..20);
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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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