A240684 Number of forests with n labeled nodes and 7 trees.

1, 28, 630, 14070, 331485, 8411634, 231354123, 6899167275, 222569372025, 7741879425280, 289297137120992, 11570476164077376, 493535471267193810, 22376155441920000000, 1074961750207964923710, 54561107576767408522752, 2918071167402563863036269

Offset: 7

Author

Alois P. Heinz, Apr 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..200

Crossrefs

Column m=7 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, 7):
seq(a(n), n=7..30);

Mathematica

Table[n^(n-14) * (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^6 + 51*n^5 + 1385*n^4 + 24885*n^3 + 303766*n^2 + 2333976*n + 8648640)/46080,{n,7,25}] (* Vaclav Kotesovec, Sep 06 2014 *)

Formula

a(n) = n^(n-14) * (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^6 + 51*n^5 + 1385*n^4 + 24885*n^3 + 303766*n^2 + 2333976*n + 8648640)/46080. - Vaclav Kotesovec, Sep 06 2014