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A119365
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Generalized Catalan numbers for triangle A119335.
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4
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1, 0, 0, 1, 6, 20, 51, 126, 392, 1513, 5877, 21054, 71270, 242463, 863590, 3193737, 11889414, 43783908, 159998493, 586908936, 2175907284, 8138471667, 30541703733, 114620380032, 430344635913, 1619584557885, 6116422089050
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(n)+A119366(n)+A119367(n)=A00108(n). Counts rooted planar n-trees whose number of leaves is divisible by 3.
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FORMULA
| a(n)=A119335(2n,n)-A119335(2n,n+1); a(n)=sum{k=0..n, if(mod(n-k,3)=0, (1/n)*C(n,k)*C(n,k+1), 0)};
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CROSSREFS
| Cf. A001263.
Sequence in context: A002415 A052515 A067117 * A001211 A122225 A027178
Adjacent sequences: A119362 A119363 A119364 * A119366 A119367 A119368
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 16 2006
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