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A145458 Exponential transform of C(n,8) = A000581.

%I A145458 #13 Feb 05 2020 15:48:12
%S A145458 1,0,0,0,0,0,0,0,1,9,45,165,495,1287,3003,6435,19305,243100,3981978,
%T A145458 49959702,498967170,4190469570,30728937690,201931408074,1213163827326,
%U A145458 6849350570700,39615797628550,296414654550300,3418235092302030
%N A145458 Exponential transform of C(n,8) = A000581.
%C A145458 a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 8 balls are seen at the top.
%C A145458 a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 8 labels.
%H A145458 Alois P. Heinz, <a href="/A145458/b145458.txt">Table of n, a(n) for n = 0..500</a>
%H A145458 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A145458 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A145458 E.g.f.: exp(exp(x)*x^8/8!).
%p A145458 a:= proc(n) option remember; `if`(n=0, 1,
%p A145458       add(binomial(n-1, j-1) *binomial(j,8) *a(n-j), j=1..n))
%p A145458     end:
%p A145458 seq(a(n), n=0..35);
%t A145458 With[{nn=30},CoefficientList[Series[Exp[Exp[x] x^8/8!],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Feb 05 2020 *)
%Y A145458 8th column of A145460, A143398.
%K A145458 nonn
%O A145458 0,10
%A A145458 _Alois P. Heinz_, Oct 10 2008