A273655 Number of forests of labeled rooted trees of height at most 1, with n labels, five of which are used for root nodes and any root may contain >= 1 labels.

52, 906, 9891, 87416, 686826, 5020092, 35006202, 236460312, 1562226237, 10158790642, 65294141913, 415967090448, 2631510433188, 16551428673528, 103578621308388, 645186720537744, 4000912828433199, 24700465510596414, 151810205132056779, 928768921758036744

Offset: 5

Author

Alois P. Heinz, May 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000

Crossrefs

Column k=5 of A143396.

Programs

Maple

a:= n-> binomial(n,5)*add(Stirling2(5,j)*j^(n-5), j=0..5):
seq(a(n), n=5..40);

Formula

E.g.f.: x^5/5! * Sum_{j=0..5} Stirling2(5,j)*exp(x)^j.

a(n) = C(n,5) * Sum_{j=0..5} Stirling2(5,j) * j^(n-5).