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%I #14 Nov 21 2017 02:42:23
%S 1,0,0,0,0,1,6,21,56,126,378,3234,34056,289575,2020018,12237225,
%T 70634928,468041756,4190274648,45557515620,499503011496,5121432107757,
%U 49183015347774,462331794763069,4579813478536296,50959878972009546
%N Exponential transform of C(n,5) = A000389.
%C a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 5 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 5 labels.
%H Alois P. Heinz, <a href="/A145455/b145455.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^5/5!).
%p a:= proc(n) option remember; `if`(n=0, 1,
%p add(binomial(n-1, j-1) *binomial(j,5) *a(n-j), j=1..n))
%p end:
%p seq(a(n), n=0..30);
%t With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]*x^5/5!], {x, 0, nmax}], x]] (* _G. C. Greubel_, Nov 21 2017 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)*x^5/5!))) \\ _G. C. Greubel_, Nov 21 2017
%Y 5th column of A145460, A143398.
%K nonn
%O 0,7
%A _Alois P. Heinz_, Oct 10 2008
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