cp's OEIS Frontend

A240682 Number of forests with n labeled nodes and 5 trees.

%I A240682 #9 Sep 06 2014 14:59:17
%S A240682 1,15,210,3220,55755,1092105,24048255,590412240,16027796070,
%T A240682 477411574640,15495339234375,544652100894720,20619226977792170,
%U A240682 836670560604157440,36232055577668433690,1668081561600000000000,81363801140161673297535,4191692026268767965880320
%N A240682 Number of forests with n labeled nodes and 5 trees.
%H A240682 Alois P. Heinz, <a href="/A240682/b240682.txt">Table of n, a(n) for n = 5..200</a>
%F A240682 a(n) = n^(n-10) * (n-4)*(n-3)*(n-2)*(n-1)*(n^4 + 30*n^3 + 451*n^2 + 3846*n + 15120)/384. - _Vaclav Kotesovec_, Sep 06 2014
%p A240682 T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
%p A240682       `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
%p A240682        T(n-j, m-1), j=1..n-m+1))))
%p A240682     end:
%p A240682 a:= n-> T(n, 5):
%p A240682 seq(a(n), n=5..30);
%t A240682 Table[n^(n-10) * (n-4)*(n-3)*(n-2)*(n-1)*(n^4 + 30*n^3 + 451*n^2 + 3846*n + 15120)/384,{n,5,20}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A240682 Column m=5 of A105599. A diagonal of A138464.
%K A240682 nonn
%O A240682 5,2
%A A240682 _Alois P. Heinz_, Apr 10 2014