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Search: id:A118929
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| A118929 |
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a(n) = Sum_{k=0..[n/2]} 2^(n-2*k-1)*C(n-1,2*k)*C(2*k,k)/(k+1)*a(k), with a(0)=1. |
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+0
1
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| 1, 1, 2, 5, 14, 44, 152, 569, 2270, 9524, 41576, 187432, 868144, 4117216, 19945408, 98523013, 495521686, 2534420852, 13167361256, 69417635240, 370991119792, 2008036459744, 10997771773888, 60896581502800, 340633178891872
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OFFSET
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0,3
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COMMENT
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Invariant column vector V under matrix product A091894*V = V: a(n) = Sum_{k=0,[n/2]} A091894(n,k)*a(k), where A091894(n,k) = number of Dyck paths of semilength n, having k ddu's [here u=(1,1) and d=(1,-1)].
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, 2^(n-2*k-1)*binomial(n-1, 2*k)*binomial(2*k, k)/(k+1)*a(k)))}
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CROSSREFS
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Cf. A091894.
Sequence in context: A137557 A119021 A002890 this_sequence A081558 A014322 A095148
Adjacent sequences: A118926 A118927 A118928 this_sequence A118930 A118931 A118932
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 06 2006
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