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A206429
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Triangular array read by rows. T(n,k) is the number of rooted labeled trees on n nodes such that the root node has degree k. n>=2, 1<=k<=n-1.
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7
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2, 6, 3, 36, 24, 4, 320, 240, 60, 5, 3750, 3000, 900, 120, 6, 54432, 45360, 15120, 2520, 210, 7, 941192, 806736, 288120, 54880, 5880, 336, 8, 18874368, 16515072, 6193152, 1290240, 161280, 12096, 504, 9, 430467210, 382637520, 148803480, 33067440, 4592700, 408240, 22680, 720
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OFFSET
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2,1
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LINKS
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FORMULA
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E.g.f.: x*exp(y * T(x)) where T(x) is the e.g.f. for A000169.
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EXAMPLE
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Triangle begins:
2;
6 3;
36 24 4;
320 240 60 5;
3750 3000 900 120 6;
54432 45360 15120 2520 210 7;
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MATHEMATICA
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nn=10; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; f[list_]:=Select[list, #>0&]; Map[f, Drop[Transpose[Table[Range[0, nn]!CoefficientList[Series[x t^k/k!, {x, 0, nn}], x], {k, 1, 8}]], 2]]//Flatten
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PROG
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(PARI) T(n)={my(f=serreverse(x*exp(-x + O(x^n)))); [Vecrev(p/y) | p<-Vec(serlaplace(x*exp(y*f) - x))]}
{ my(A=T(7)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 22 2020
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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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