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A071716
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Expansion of (1+x^2*C)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
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4
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1, 1, 3, 7, 19, 56, 174, 561, 1859, 6292, 21658, 75582, 266798, 950912, 3417340, 12369285, 45052515, 165002460, 607283490, 2244901890, 8331383610, 31030387440, 115948830660, 434542177290, 1632963760974, 6151850548776
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = number of lattice paths of n up steps and n down steps that start at the origin with an up step and do not cross the x-axis except possibly at (2n-2,0). - David Callan (callan(AT)stat.wisc.edu), Mar 14 2004
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FORMULA
| a(n) = C_n + C_(n-1) (Catalan numbers). - David Callan (callan(AT)stat.wisc.edu), Mar 14 2004
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CROSSREFS
| Essentially the same as A005807.
Sequence in context: A183120 A100702 A147586 * A188625 A005506 A201169
Adjacent sequences: A071713 A071714 A071715 * A071717 A071718 A071719
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2002
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