cp's OEIS Frontend

A143406 Number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains a nonempty set of labels of equal size, also row sums of A143398.

%I A143406 #16 Mar 29 2016 20:44:13
%S A143406 1,1,4,14,55,252,1319,7737,50040,351636,2659375,21519027,185279186,
%T A143406 1688183135,16206401020,163376811610,1724624368377,19011582728772,
%U A143406 218312877627483,2605840967052663,32271957793959066,413991491885677105,5492584623675060620
%N A143406 Number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains a nonempty set of labels of equal size, also row sums of A143398.
%H A143406 Alois P. Heinz, <a href="/A143406/b143406.txt">Table of n, a(n) for n = 0..530</a>
%H A143406 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A143406 a(n) = 1 if n=0 and a(n) = n! * Sum_{k=1..n} Sum_{i=1..floor(n/k)} i^(n-k*i)/ ((n-k*i)!*i!*k!^i) else.
%e A143406 a(2) = 4, because 4 forests with 2 labels exist: {1}{2}, {1}<-2, {2}<-1, {1,2}.
%p A143406 a:= n-> if n=0 then 1 else n! * add(add(i^(n-k*i)/
%p A143406         ((n-k*i)!*i!*k!^i), i=1..floor(n/k)), k=1..n) fi:
%p A143406 seq(a(n), n=0..30);
%Y A143406 Cf. A143398, A000142.
%K A143406 nonn
%O A143406 0,3
%A A143406 _Alois P. Heinz_, Aug 12 2008