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 A240686 Number of forests with n labeled nodes and 9 trees. 3

%I

%S 1,45,1485,45540,1402830,44837793,1508782275,53789959080,

%T 2036262886515,81857181636945,3490649483399793,157637380245930000,

%U 7524305274666328785,378816067488484478160,20074256751067210380645,1117410784286881766178816,65207052558569641113281250

%N Number of forests with n labeled nodes and 9 trees.

%H Alois P. Heinz, <a href="/A240686/b240686.txt">Table of n, a(n) for n = 9..200</a>

%F 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

%p T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,

%p `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*

%p T(n-j, m-1), j=1..n-m+1))))

%p end:

%p a:= n-> T(n, 9):

%p seq(a(n), n=9..30);

%t 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 *)

%Y Column m=9 of A105599. A diagonal of A138464.

%K nonn

%O 9,2

%A _Alois P. Heinz_, Apr 10 2014

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Last modified January 20 23:29 EST 2020. Contains 331104 sequences. (Running on oeis4.)