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Search: id:A045741
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| A045741 |
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Number of edges in all noncrossing connected graphs on nodes on a circle. |
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+0
2
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| 1, 9, 82, 765, 7266, 69930, 679764, 6659037, 65635570, 650194974, 6467730204, 64562259762, 646399361076, 6488447895540, 65276186864232, 657998685456093, 6644370824416530, 67198463606576790, 680568874690989900
(list; graph; listen)
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OFFSET
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2,2
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LINKS
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Sen-Peng Eu, Shu-Chung Liu and Yeong-Nan Yeh, On the congruences of some combinatorial numbers, Stud. Appl. Math. vol. 116 (2006) pp. 135-144
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FORMULA
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sum(k*binomial(3*n-3, n+k)*binomial(k-1, k-n+1), k=n-1..2*n)/(n-1)
a(n) = 1 mod 3 if n in A103457; a(n) = 0 mod 3 otherwise [Eu et al.]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 27 2008
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MAPLE
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A045741 := proc(n) local k ; add(binomial(3*n-3, n+k)*binomial(k, n-1), k=0..2*n-3) ; end: seq(A045741(n), n=2..20) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 27 2008
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CROSSREFS
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Cf. A007297.
Sequence in context: A163460 A081191 A060531 this_sequence A110567 A041146 A015497
Adjacent sequences: A045738 A045739 A045740 this_sequence A045742 A045743 A045744
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu)
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