A240686 Number of forests with n labeled nodes and 9 trees.

1, 45, 1485, 45540, 1402830, 44837793, 1508782275, 53789959080, 2036262886515, 81857181636945, 3490649483399793, 157637380245930000, 7524305274666328785, 378816067488484478160, 20074256751067210380645, 1117410784286881766178816, 65207052558569641113281250

Offset: 9

Author

Alois P. Heinz, Apr 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..200

Crossrefs

Column m=9 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, 9):
seq(a(n), n=9..30);

Mathematica

Table[n^(n-18) * (n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^8 + 76*n^7 + 3122*n^6 + 88760*n^5 + 1873921*n^4 + 29555596*n^3 + 334746252*n^2 + 2455095600*n + 8821612800)/10321920,{n,9,30}] (* Vaclav Kotesovec, Sep 06 2014 *)

Formula

a(n) = n^(n-18) * (n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^8 + 76*n^7 + 3122*n^6 + 88760*n^5 + 1873921*n^4 + 29555596*n^3 + 334746252*n^2 + 2455095600*n + 8821612800)/10321920. - Vaclav Kotesovec, Sep 06 2014