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A036506
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Number of labeled 4-trees with n nodes.
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9
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0, 0, 0, 1, 1, 15, 455, 20230, 1166886, 82031250, 6768679170, 639276644655, 67876292150095, 7992910154350121, 1032869077119140625, 145221924661653841820, 22060305511905816000860, 3599313659344525384083060, 627583654087024080928783956
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OFFSET
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1,6
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REFERENCES
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F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=4.
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LINKS
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FORMULA
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a(n) = C(n,4)*(4*n-15)^(n-6).
Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
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PROG
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(Python)
def A036506(n): return int(n*(n - 3)*(n - 2)*(n - 1)*(4*n - 15)**(n - 6)//24) # Chai Wah Wu, Feb 03 2022
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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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