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A240685
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Number of forests with n labeled nodes and 8 trees.
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3
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1, 36, 990, 26070, 705375, 20151846, 614506893, 20073049425, 702495121185, 26300384653400, 1050925859466912, 44702294310795888, 2018603140944000000, 96508616036970572820, 4872478522317533107200, 259140537891648535707618, 14485018396686799073181696
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OFFSET
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8,2
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LINKS
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FORMULA
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a(n) = n^(n-16) * (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^7 + 63*n^6 + 2135*n^5 + 49245*n^4 + 816256*n^3 + 9527868*n^2 + 71254800*n + 259459200)/645120. - 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, 8):
seq(a(n), n=8..30);
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MATHEMATICA
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Table[n^(n-16) * (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^7 + 63*n^6 + 2135*n^5 + 49245*n^4 + 816256*n^3 + 9527868*n^2 + 71254800*n + 259459200)/645120, {n, 8, 25}] (* 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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