A273654 Number of forests of labeled rooted trees of height at most 1, with n labels, four of which are used for root nodes and any root may contain >= 1 labels.

15, 185, 1485, 9905, 59850, 341082, 1872990, 10032990, 52814025, 274436305, 1411449039, 7195628895, 36390053700, 182622509860, 909578754540, 4496410556268, 22062707386875, 107464431586995, 519700280676885, 2495827315731365, 11905791978208590, 56429414876395550

Offset: 4

Author

Alois P. Heinz, May 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000

Crossrefs

Column k=4 of A143396.

Programs

Maple

a:= n-> binomial(n,4)*add(Stirling2(4,j)*j^(n-4), j=0..4):
seq(a(n), n=4..40);

Formula

E.g.f.: x^4/4! * Sum_{j=0..4} Stirling2(4,j)*exp(x)^j.

a(n) = C(n,4) * Sum_{j=0..4} Stirling2(4,j) * j^(n-4).