A273656 Number of forests of labeled rooted trees of height at most 1, with n labels, six of which are used for root nodes and any root may contain >= 1 labels.

203, 4718, 66808, 750120, 7370580, 66562188, 568136184, 4663350120, 37228965774, 291297376370, 2245876801168, 17126594554160, 129527848747752, 973416393927768, 7278979868039760, 54211596845506800, 402386221073227314, 2977842560384800878, 21977111826224423176

Offset: 6

Author

Alois P. Heinz, May 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000

Crossrefs

Column k=6 of A143396.

Programs

Maple

a:= n-> binomial(n,6)*add(Stirling2(6,j)*j^(n-6), j=0..6):
seq(a(n), n=6..40);

Formula

E.g.f.: x^6/6! * Sum_{j=0..6} Stirling2(6,j)*exp(x)^j.

a(n) = C(n,6) * Sum_{j=0..6} Stirling2(6,j) * j^(n-6).