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Search: id:A085614
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| A085614 |
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Elementary arches of size n. |
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+0
2
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| 1, 3, 16, 105, 768, 6006, 49152, 415701, 3604480, 31870410, 286261248, 2604681690, 23957864448, 222399744300, 2080911654912, 19604537460045, 185813170126848, 1770558814528770, 16951376923852800, 162984598242674670
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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G.f. is series reversion of x-3x^2+2x^3.
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LINKS
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F. Cazals, Combinatorics of Non-Crossing Configurations, Studies in Automatic Combinatorics, Volume II (1997).
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FORMULA
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a(n) = 2^n(3n)!!/((n+1)! n!!) - Maxim Krikun (krikun(AT)iecn.u-nancy.fr), May 25 2007
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MAPLE
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with(combstruct); ar := {EA = Union(Sequence(EA, card >= 2), Prod(Z, Sequence(EA), Sequence(EA))), C=Union(Z, Prod(Z, Z, Sequence(EA), Sequence(EA), Sequence(Union(Sequence(EA, card>=1), Prod(Z, Sequence(EA), Sequence(EA))))))}; seq(count([EA, ar], size=i), i=1..20);
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PROGRAM
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(PARI) a(n)=if(n<1, 0, polcoeff(serreverse(x-3*x^2+2*x^3+x*O(x^n)), n))
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CROSSREFS
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Sequence in context: A074542 A105622 A110903 this_sequence A014304 A063548 A157452
Adjacent sequences: A085611 A085612 A085613 this_sequence A085615 A085616 A085617
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jul 10 2003
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