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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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7
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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
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OFFSET
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0,3
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COMMENTS
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a(n) is the 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, Mar 14 2004
a(n) is the number of parking functions of size n avoiding the patterns 132, 213, 231, and 321. - Lara Pudwell, Apr 10 2023
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LINKS
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FORMULA
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D-finite with recurrence (n+1)*a(n) +(-3*n+1)*a(n-1) +2*(-2*n+5)*a(n-2)=0, n>=3 - R. J. Mathar, Aug 25 2013
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MATHEMATICA
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Join[{1, 1}, Total/@Partition[CatalanNumber[Range[30]], 2, 1]] (* Harvey P. Dale, Mar 23 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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