A240687 Number of forests with n labeled nodes and 10 trees.

1, 55, 2145, 75790, 2637635, 93783690, 3467403940, 134463763720, 5491244257785, 236503301350745, 10742799174110575, 514243815022230930, 25908948794088640280, 1371861202568610407885, 76216658109172817448960, 4435598473883166992187500, 269963484584876515488140800

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..200

Formula

a(n) = n^(n-20) * (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^9 + 90*n^8 + 4386*n^7 + 149436*n^6 + 3859401*n^5 + 77149170*n^4 + 1176873076*n^3 + 13044397176*n^2 + 94273812000*n + 335221286400)/185794560. - 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, 10):
seq(a(n), n=10..30);

Mathematica

Table[n^(n-20) * (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^9 + 90*n^8 + 4386*n^7 + 149436*n^6 + 3859401*n^5 + 77149170*n^4 + 1176873076*n^3 + 13044397176*n^2 + 94273812000*n + 335221286400)/185794560, {n, 10, 30}] (* Vaclav Kotesovec, Sep 06 2014 *)

Crossrefs

Column m=10 of A105599. A diagonal of A138464.

Sequence in context: A275942 A217758 A346325 * A053113 A012048 A215860

Adjacent sequences: A240684 A240685 A240686 * A240688 A240689 A240690

Keyword

nonn

Author

Alois P. Heinz, Apr 10 2014

Status

approved