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A240681 Number of forests with n labeled nodes and 4 trees. 3
1, 10, 105, 1295, 18865, 320544, 6258000, 138437310, 3428282880, 94059655690, 2833936641536, 93055995703125, 3308477732618240, 126642365068676240, 5193315990469140480, 227160198500847385884, 10557603840000000000000, 519578655591970045435770 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..200

FORMULA

a(n) = n^(n-8) * (n-3)*(n-2)*(n-1)*(n^3 + 21*n^2 + 202*n + 840)/48. - 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, 4):

seq(a(n), n=4..30);

MATHEMATICA

Table[n^(n-8) * (n-3)*(n-2)*(n-1)*(n^3 + 21*n^2 + 202*n + 840)/48, {n, 4, 20}] (* Vaclav Kotesovec, Sep 06 2014 *)

CROSSREFS

Column m=4 of A105599. A diagonal of A138464.

Sequence in context: A079515 A024131 A000457 * A113348 A193274 A068883

Adjacent sequences:  A240678 A240679 A240680 * A240682 A240683 A240684

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 10 2014

STATUS

approved

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)