A145457 - OEIS

%I #23 Jun 11 2018 11:03:08

%S 1,0,0,0,0,0,0,1,8,36,120,330,792,1716,5148,57915,835120,9354488,

%T 84047184,638567124,4256855760,25607297880,144863655024,869425029957,

%U 7081044528888,83816629147900,1131047706331400,14634713798592030,173380501913172840

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

%C 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 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 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 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^7/7!).

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

%p       add(binomial(n-1, j-1) *binomial(j,7) *a(n-j), j=1..n))

%p     end:

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

%t a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n - 1, j - 1] *Binomial[j, 7]* a[n - j], {j, 1, n}]];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 11 2018, after _Alois P. Heinz_ *)

%Y 7th column of A145460, A143398.

%K nonn

%O 0,9

%A _Alois P. Heinz_, Oct 10 2008