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A273653
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Number of forests of labeled rooted trees of height at most 1, with n labels, three of which are used for root nodes and any root may contain >= 1 labels.
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2
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5, 40, 220, 1040, 4550, 19040, 77448, 308640, 1209450, 4668400, 17766892, 66718288, 247397150, 906584000, 3285842960, 11788924992, 41902786770, 147668053200, 516315206260, 1792304871280, 6180666260230, 21184488791840, 72205377800600, 244837696095200
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OFFSET
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3,1
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LINKS
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FORMULA
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E.g.f.: x^3/3! * Sum_{j=0..3} Stirling2(3,j)*exp(x)^j.
a(n) = C(n,3) * Sum_{j=0..3} Stirling2(3,j) * j^(n-3).
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MAPLE
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a:= n-> binomial(n, 3)*add(Stirling2(3, j)*j^(n-3), j=0..3):
seq(a(n), n=3..40);
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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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