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A240686 Number of forests with n labeled nodes and 9 trees. 3
1, 45, 1485, 45540, 1402830, 44837793, 1508782275, 53789959080, 2036262886515, 81857181636945, 3490649483399793, 157637380245930000, 7524305274666328785, 378816067488484478160, 20074256751067210380645, 1117410784286881766178816, 65207052558569641113281250 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

LINKS

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

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

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 *)

CROSSREFS

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

Sequence in context: A035521 A107399 A053112 * A014940 A273436 A049397

Adjacent sequences:  A240683 A240684 A240685 * A240687 A240688 A240689

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 10 2014

STATUS

approved

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)