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A143657
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Number of 4-noncrossing stack-free partial matching without 1-arcs.
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0
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1, 1, 2, 5, 12, 32, 95, 301, 1001, 3495, 12708, 47932, 186581, 747619, 3073207
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OFFSET
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1,3
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COMMENTS
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This sequence is the second row of Jin and Reidys table, p. 15; the first row, number of 3-noncrossing stack-free partial matching without 1-arcs, is A132441.
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LINKS
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FORMULA
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a(n) = C_4(n,h) = SUM[b=0..{h-1}](-1)^{h-b-1}{h-1 Choose b}{T}_4(h-2h+2b+2,b+1); where the T function is defined in Jin and Reidys.
Asymptotically a(n) ~ (1.217 * 10^7)*(n^(-21/2))*(3.0382^n).
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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