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A145457 Exponential transform of C(n,7) = A000580.

%I A145457 #23 Jun 11 2018 11:03:08
%S A145457 1,0,0,0,0,0,0,1,8,36,120,330,792,1716,5148,57915,835120,9354488,
%T A145457 84047184,638567124,4256855760,25607297880,144863655024,869425029957,
%U A145457 7081044528888,83816629147900,1131047706331400,14634713798592030,173380501913172840
%N A145457 Exponential transform of C(n,7) = A000580.
%C A145457 a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 7 balls are seen at the top.
%C A145457 a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 7 labels.
%H A145457 Seiichi Manyama, <a href="/A145457/b145457.txt">Table of n, a(n) for n = 0..556</a> (terms 0..200 from Alois P. Heinz)
%H A145457 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A145457 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A145457 E.g.f.: exp(exp(x)*x^7/7!).
%p A145457 a:= proc(n) option remember; `if`(n=0, 1,
%p A145457       add(binomial(n-1, j-1) *binomial(j,7) *a(n-j), j=1..n))
%p A145457     end:
%p A145457 seq(a(n), n=0..30);
%t A145457 a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n - 1, j - 1] *Binomial[j, 7]* a[n - j], {j, 1, n}]];
%t A145457 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 11 2018, after _Alois P. Heinz_ *)
%Y A145457 7th column of A145460, A143398.
%K A145457 nonn
%O A145457 0,9
%A A145457 _Alois P. Heinz_, Oct 10 2008