%I #13 Mar 16 2015 17:14:43
%S 1,0,0,0,0,0,0,0,0,1,10,55,220,715,2002,5005,11440,24310,72930,
%T 1016158,18643560,258952330,2845739820,26177047270,209411148144,
%U 1495786618975,9722602868550,58373582056075,329869586346300,1861266055353705
%N Exponential transform of C(n,9) = A000582.
%C a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 9 balls are seen at the top.
%C a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 9 labels.
%H Alois P. Heinz, <a href="/A145459/b145459.txt">Table of n, a(n) for n = 0..500</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F E.g.f.: exp(exp(x)*x^9/9!).
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(binomial(n-1, j-1) *binomial(j,9) *a(n-j), j=1..n))
%p end:
%p seq(a(n), n=0..35);
%Y 9th column of A145460, A143398.
%K nonn
%O 0,11
%A _Alois P. Heinz_, Oct 10 2008