A240685 Number of forests with n labeled nodes and 8 trees.

1, 36, 990, 26070, 705375, 20151846, 614506893, 20073049425, 702495121185, 26300384653400, 1050925859466912, 44702294310795888, 2018603140944000000, 96508616036970572820, 4872478522317533107200, 259140537891648535707618, 14485018396686799073181696

Offset: 8

Author

Alois P. Heinz, Apr 10 2014

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)

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