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A132051
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Sixth column of triangle A035342.
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1
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1, 63, 2730, 103950, 3786615, 137162025, 5039703900, 189883593900, 7381251402525, 297032627967075, 12395985005353950, 536910000482705850, 24139951470365605875, 1126381171697414758125, 54517938404202375102000
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OFFSET
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6,2
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COMMENTS
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a(n), n >= 6, enumerates unordered n-vertex forests composed of six plane increasing ternary trees. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.
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LINKS
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FORMULA
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E.g.f.: ((x*c(x/2)*(1-2*x)^(-1/2))^6)/6!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
E.g.f.: (-1+(1-2*x)^(-1/2))^6/6!.
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MATHEMATICA
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Drop[With[{nn=20}, CoefficientList[Series[(-1+1/Sqrt[1-2x])^6/720, {x, 0, nn}], x] Range[0, nn]!], 6] (* Harvey P. Dale, May 27 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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