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Search: id:A052121
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| A052121 |
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Triangle of coefficients of polynomials enumerating trees with n labeled nodes by inversions. |
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+0
1
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| 1, 1, 2, 1, 6, 6, 3, 1, 24, 36, 30, 20, 10, 4, 1, 120, 240, 270, 240, 180, 120, 70, 35, 15, 5, 1, 720, 1800, 2520, 2730, 2520, 2100, 1610, 1140, 750, 455, 252, 126, 56, 21, 6, 1, 5040, 15120, 25200, 31920, 34230, 32970, 29400, 24640, 19600, 14840, 10696, 7336
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.48.
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FORMULA
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Sum_{k=1..binomial(k-1, 2)} T(n, k)=A000272(n). Sum_{k=1..binomial(k-1, 2)} (-1)^k*T(n, k)=A000111(n-1).
E.g.f.: (y-1)*log(Sum_{n >= 0} (y-1)^(-n)*y^binomial(n, 2)*x^n/n!.
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EXAMPLE
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1; 1; 2 1; 6 6 3 1; 24 36 30 20 10 4 1; ...
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CROSSREFS
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Cf. A000272, A000111.
Sequence in context: A090582 A079641 A075181 this_sequence A117965 A111646 A117753
Adjacent sequences: A052118 A052119 A052120 this_sequence A052122 A052123 A052124
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KEYWORD
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nonn,easy,nice,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 23 2000
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EXTENSIONS
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Formulae and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 06 2001
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