A273658 Number of forests of labeled rooted trees of height at most 1, with n labels, eight of which are used for root nodes and any root may contain >= 1 labels.

4140, 153063, 3315645, 55239525, 786082275, 10081916559, 120278261103, 1361959159275, 14838761544750, 157056039953670, 1626124163724918, 16555067600440590, 166368479811851850, 1655233308679110930, 16341232769733507570, 160366537782578273850

Offset: 8

Author

Alois P. Heinz, May 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A143396.

Programs

Maple

a:= n-> binomial(n,8)*add(Stirling2(8,j)*j^(n-8), j=0..8):
seq(a(n), n=8..40);

Formula

E.g.f.: x^8/8! * Sum_{j=0..8} Stirling2(8,j)*exp(x)^j.

a(n) = C(n,8) * Sum_{j=0..8} Stirling2(8,j) * j^(n-8).