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A145456 Exponential transform of C(n,6) = A000579.

%I A145456 #13 Apr 14 2018 09:58:07
%S A145456 1,0,0,0,0,0,1,7,28,84,210,462,1386,13728,171171,1686685,13461448,
%T A145456 91495768,551777772,3142726692,19787406360,172188951144,1999835600301,
%U A145456 24655331721867,285725747201356,3034790658153100,29876851476502030
%N A145456 Exponential transform of C(n,6) = A000579.
%C A145456 a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 6 balls are seen at the top.
%C A145456 a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 6 labels.
%H A145456 Alois P. Heinz, <a href="/A145456/b145456.txt">Table of n, a(n) for n = 0..500</a>
%H A145456 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A145456 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A145456 E.g.f.: exp(exp(x)*x^6/6!).
%p A145456 a:= proc(n) option remember; `if`(n=0, 1,
%p A145456       add(binomial(n-1, j-1) *binomial(j,6) *a(n-j), j=1..n))
%p A145456     end:
%p A145456 seq(a(n), n=0..30);
%t A145456 With[{nn=30},CoefficientList[Series[Exp[Exp[x] x^6/6!],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 14 2018 *)
%Y A145456 6th column of A145460, A143398.
%K A145456 nonn
%O A145456 0,8
%A A145456 _Alois P. Heinz_, Oct 10 2008