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A220233
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Triangular array read by rows. T(n,k) is the number of labeled rooted trees of height at most 2 with exactly k leaves at a distance 1 from the root, n>=1, 0<=k<=n-1.
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0
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0, 0, 2, 6, 0, 3, 12, 24, 0, 4, 80, 60, 60, 0, 5, 390, 480, 180, 120, 0, 6, 2352, 2730, 1680, 420, 210, 0, 7, 15176, 18816, 10920, 4480, 840, 336, 0, 8, 106416, 136584, 84672, 32760, 10080, 1512, 504, 0, 9, 801450, 1064160, 682920, 282240, 81900, 20160, 2520, 720, 0, 10
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: x*(exp(x*(exp(x) -1 + y)) - 1 + y) (letting T(1,1)=1).
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EXAMPLE
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Triangle T(n,k) begins:
0;
0, 2;
6, 0, 3;
12, 24, 0, 4;
80, 60, 60, 0, 5;
390, 480, 180, 120, 0, 6;
2352, 2730, 1680, 420, 210, 0, 7;
...
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MATHEMATICA
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nn=7; f[list_]:=Select[list, #>0&]; a=x (Exp[x]-1+y); Prepend[Drop[Map[Insert[#, 0, -2]&, Map[f, Range[0, nn]!CoefficientList[Series[x (Exp[a]-1+y), {x, 0, nn}], {x, y}]]], 2], {0}]//Grid
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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