A240681 Number of forests with n labeled nodes and 4 trees.

1, 10, 105, 1295, 18865, 320544, 6258000, 138437310, 3428282880, 94059655690, 2833936641536, 93055995703125, 3308477732618240, 126642365068676240, 5193315990469140480, 227160198500847385884, 10557603840000000000000, 519578655591970045435770

Offset: 4

Author

Alois P. Heinz, Apr 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..200

Crossrefs

Column m=4 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, 4):
seq(a(n), n=4..30);

Mathematica

Table[n^(n-8) * (n-3)*(n-2)*(n-1)*(n^3 + 21*n^2 + 202*n + 840)/48,{n,4,20}] (* Vaclav Kotesovec, Sep 06 2014 *)

Formula

a(n) = n^(n-8) * (n-3)*(n-2)*(n-1)*(n^3 + 21*n^2 + 202*n + 840)/48. - Vaclav Kotesovec, Sep 06 2014