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A240687
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Number of forests with n labeled nodes and 10 trees.
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3
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1, 55, 2145, 75790, 2637635, 93783690, 3467403940, 134463763720, 5491244257785, 236503301350745, 10742799174110575, 514243815022230930, 25908948794088640280, 1371861202568610407885, 76216658109172817448960, 4435598473883166992187500, 269963484584876515488140800
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OFFSET
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10,2
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LINKS
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FORMULA
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a(n) = n^(n-20) * (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^9 + 90*n^8 + 4386*n^7 + 149436*n^6 + 3859401*n^5 + 77149170*n^4 + 1176873076*n^3 + 13044397176*n^2 + 94273812000*n + 335221286400)/185794560. - Vaclav Kotesovec, Sep 06 2014
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MAPLE
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T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
`if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
T(n-j, m-1), j=1..n-m+1))))
end:
a:= n-> T(n, 10):
seq(a(n), n=10..30);
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MATHEMATICA
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Table[n^(n-20) * (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^9 + 90*n^8 + 4386*n^7 + 149436*n^6 + 3859401*n^5 + 77149170*n^4 + 1176873076*n^3 + 13044397176*n^2 + 94273812000*n + 335221286400)/185794560, {n, 10, 30}] (* Vaclav Kotesovec, Sep 06 2014 *)
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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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