A240682 Number of forests with n labeled nodes and 5 trees.

1, 15, 210, 3220, 55755, 1092105, 24048255, 590412240, 16027796070, 477411574640, 15495339234375, 544652100894720, 20619226977792170, 836670560604157440, 36232055577668433690, 1668081561600000000000, 81363801140161673297535, 4191692026268767965880320

Offset: 5

Author

Alois P. Heinz, Apr 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..200

Crossrefs

Column m=5 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, 5):
seq(a(n), n=5..30);

Mathematica

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 *)

Formula

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