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Search: id:A165976
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| A165976 |
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Number of sequences of n pairs of balanced brackets of three types, round, square, and angle, such that no square brackets are allowed inside matching round brackets. |
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+0
1
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| 1, 3, 17, 117, 887, 7131, 59661, 513897, 4526603, 40588263, 369277481, 3400840845, 31644776383, 297079014771, 2810553697989, 26770090211793, 256510096740243, 2470981627433919, 23916768109136289, 232485664356533877
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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O.f.g.: ( 1 - x*G(2*x) - sqrt( (1 - x*G(2*x))^2 - 8*x ) )/4/x = (3 + sqrt(1-8*x) - sqrt(10 - 136*x + 6*sqrt(1-8*x)))/16/x, where G(x)=(1-sqrt(1-4*x))/(2*x) is o.g.f. for Catalan numbers A000108.
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CROSSREFS
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Sequence in context: A112111 A074554 A074544 this_sequence A121572 A074543 A129115
Adjacent sequences: A165973 A165974 A165975 this_sequence A165977 A165978 A165979
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxale(AT)gmail.com), Oct 02 2009
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