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Search: id:A025174
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| 0, 1, 5, 28, 165, 1001, 6188, 38760, 245157, 1562275, 10015005, 64512240, 417225900, 2707475148, 17620076360, 114955808528, 751616304549, 4923689695575, 32308782859535, 212327989773900, 1397281501935165
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of standard tableaux of shape (2n-1,n). Example: a(2)=5 because in the top row we can have 123, 124, 125, 134, or 135. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 23 2004
Number of peaks in all generalized {(1,2),(1,-1)}-Dyck paths of length 3n.
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FORMULA
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G.f.: zg^2/(1-3zg^2), where g=g(z) is given by g=1+zg^3, g(0)=1, i.e. (in Maple command) g := 2*sin(arcsin(3*sqrt(3*z)/2)/3)/sqrt(3*z); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 22 2003
a(n)=sum{k=0..n, ((3k+1)/(2n+k+1))C(3n, 2n+k)*A001045(k)}; - Paul Barry (pbarry(AT)wit.ie), Oct 07 2005
Hankel transform of a(n+1) is A005156(n+1). - Paul Barry (pbarry(AT)wit.ie), Apr 14 2008
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MAPLE
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with(combinat):seq(numbcomp(3*i, i), i=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2007
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MATHEMATICA
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Table[ GegenbauerC[ n, n, 1 ]/2, {n, 0, 24} ]
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CROSSREFS
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Sequence in context: A005785 A027912 A090040 this_sequence A083316 A027284 A069731
Adjacent sequences: A025171 A025172 A025173 this_sequence A025175 A025176 A025177
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KEYWORD
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nonn,easy
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AUTHOR
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w.meeussen (wouter.meeussen(AT)pandora.be), Emeric Deutsch (deutsch(AT)duke.poly.edu)
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