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A026004
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a(n) = T(3n+1,n), where T = Catalan triangle (A008315).
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5
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1, 3, 14, 75, 429, 2548, 15504, 95931, 600875, 3798795, 24192090, 154969620, 997490844, 6446369400, 41802112192, 271861216539, 1772528290407, 11582393855305, 75831424919250, 497337483739635, 3266814940064445
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of standard tableaux of shape (2n+1,n). Example: a(1)=3 because in the top row we can have 134, 124, or 123 (but not 234). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 23 2004
Number of noncrossing forests with n+2 vertices and two components. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 31 2004
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REFERENCES
| P. Flajolet and M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math. 204 (1999), 203-229.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
| (n+2)/(2*n+2) * C(3*n+1, n). - R. Stephan, Apr 30 2004
G.f.: ((sqrt(x)*sin(2/3*arcsin((3*sqrt(3)*sqrt(x))/2)))/sqrt(4/3-9*x)-cos(1/3*arccos(1-(27*x)/2))+1)/(3*x). [Conjectured by Harvey P. Dale, June 30 2011]
G.f.: (2*g-1)/((3*g-1)*(g-1)^2) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 09 2011
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MATHEMATICA
| Table[(n+2)/(2n+2)Binomial[3n+1, n], {n, 0, 20}] (* From Harvey P. Dale, June 29 2011 *)
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CROSSREFS
| Cf. A045722.
Sequence in context: A080238 A074549 A126122 * A200718 A063016 A133798
Adjacent sequences: A026001 A026002 A026003 * A026005 A026006 A026007
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from R. Stephan, Apr 30 2004
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