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A102318
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A mean binomial transform of the Catalan numbers.
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0
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1, 1, 3, 8, 27, 97, 373, 1493, 6163, 26027, 111897, 488006, 2153429, 9596199, 43121211, 195165576, 888861555, 4070582971, 18732710281, 86584519280, 401776434017, 1870983991035, 8740907398527, 40956401225597
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Average of binomial and inverse binomial transforms of the Catalan numbers A000108.
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FORMULA
| G.f.: (2-sqrt((1-3x)/(1+x))-sqrt((1-5x)/(1-x)))/(4x); a(n)=sum{k=0..floor(n/2), binomial(n, 2k)C(n-2k)}; a(n)=sum{k=0..n, binomial(n, k)C(k)(1+(-1)^(n-k))/2}.
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CROSSREFS
| Sequence in context: A148843 A148844 A145760 * A102206 A110886 A104854
Adjacent sequences: A102315 A102316 A102317 * A102319 A102320 A102321
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 04 2005
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