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A240683 Number of forests with n labeled nodes and 6 trees. 3
1, 21, 378, 7056, 143325, 3207897, 79170399, 2146836978, 63641666088, 2051450651250, 71530799628288, 2684845732979592, 107992630908804096, 4636019437800293718, 211623646464000000000, 10237455825414473977524, 523244238837133507448832, 28177157277452320985386539 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..200

FORMULA

a(n) = n^(n-12) * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^5 + 40*n^4 + 835*n^3 + 10960*n^2 + 87636*n + 332640)/3840. - 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, 6):

seq(a(n), n=6..30);

MATHEMATICA

Table[n^(n-12) * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^5 + 40*n^4 + 835*n^3 + 10960*n^2 + 87636*n + 332640)/3840, {n, 6, 25}] (* Vaclav Kotesovec, Sep 06 2014 *)

CROSSREFS

Column m=6 of A105599. A diagonal of A138464.

Sequence in context: A134494 A004370 A001881 * A108740 A297455 A256178

Adjacent sequences:  A240680 A240681 A240682 * A240684 A240685 A240686

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 10 2014

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)