A273659 Number of forests of labeled rooted trees of height at most 1, with n labels, nine of which are used for root nodes and any root may contain >= 1 labels.

21147, 948280, 24564100, 483787480, 8061693640, 120120836836, 1653807555400, 21489660580960, 267385444371760, 3218688299529560, 37768351403903120, 434451231603262640, 4920317819371507280, 55047363589643246360, 609969295304994614000, 6708182596868603027936

Offset: 9

Author

Alois P. Heinz, May 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..1000

Crossrefs

Column k=9 of A143396.

Programs

Maple

a:= n-> binomial(n,9)*add(Stirling2(9,j)*j^(n-9), j=0..9):
seq(a(n), n=9..40);

Formula

E.g.f.: x^9/9! * Sum_{j=0..9} Stirling2(9,j)*exp(x)^j.

a(n) = C(n,9) * Sum_{j=0..9} Stirling2(9,j) * j^(n-9).