A145453 - OEIS

%I #25 Sep 28 2017 07:46:12

%S 1,0,0,1,4,10,30,175,1176,7084,42120,286605,2270180,19213766,

%T 166326524,1497096055,14374680880,147259920760,1582837679056,

%U 17659771122969,204674606377140,2473357218561250,31148510170120420,407154732691440811,5504706823227724904

%N Exponential transform of binomial(n,3) = A000292(n-2).

%C a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 3 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 3 labels.

%H Seiichi Manyama, <a href="/A145453/b145453.txt">Table of n, a(n) for n = 0..530</a> (terms 0..200 from Alois P. Heinz)

%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^3/3!).

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       add(binomial(n-1, j-1) *binomial(j,3) *a(n-j), j=1..n))

%p     end:

%p seq(a(n), n=0..30);

%t Table[Sum[BellY[n, k, Binomial[Range[n], 3]], {k, 0, n}], {n, 0, 25}] (* _Vladimir Reshetnikov_, Nov 09 2016 *)

%Y 3rd column of A145460, A143398.

%Y Cf. A292889, A292910.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Oct 10 2008