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A240682
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Number of forests with n labeled nodes and 5 trees.
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3
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1, 15, 210, 3220, 55755, 1092105, 24048255, 590412240, 16027796070, 477411574640, 15495339234375, 544652100894720, 20619226977792170, 836670560604157440, 36232055577668433690, 1668081561600000000000, 81363801140161673297535, 4191692026268767965880320
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OFFSET
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5,2
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LINKS
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FORMULA
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a(n) = n^(n-10) * (n-4)*(n-3)*(n-2)*(n-1)*(n^4 + 30*n^3 + 451*n^2 + 3846*n + 15120)/384. - 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, 5):
seq(a(n), n=5..30);
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MATHEMATICA
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Table[n^(n-10) * (n-4)*(n-3)*(n-2)*(n-1)*(n^4 + 30*n^3 + 451*n^2 + 3846*n + 15120)/384, {n, 5, 20}] (* 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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