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A145459 Exponential transform of C(n,9) = A000582.

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