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A240685 Number of forests with n labeled nodes and 8 trees. 3
1, 36, 990, 26070, 705375, 20151846, 614506893, 20073049425, 702495121185, 26300384653400, 1050925859466912, 44702294310795888, 2018603140944000000, 96508616036970572820, 4872478522317533107200, 259140537891648535707618, 14485018396686799073181696 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..200

FORMULA

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

MAPLE

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);

MATHEMATICA

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 *)

CROSSREFS

Column m=8 of A105599. A diagonal of A138464.

Sequence in context: A053111 A260855 A130563 * A294162 A025419 A180802

Adjacent sequences:  A240682 A240683 A240684 * A240686 A240687 A240688

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 10 2014

STATUS

approved

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Last modified May 21 02:33 EDT 2019. Contains 323431 sequences. (Running on oeis4.)