A273653 Number of forests of labeled rooted trees of height at most 1, with n labels, three of which are used for root nodes and any root may contain >= 1 labels.

5, 40, 220, 1040, 4550, 19040, 77448, 308640, 1209450, 4668400, 17766892, 66718288, 247397150, 906584000, 3285842960, 11788924992, 41902786770, 147668053200, 516315206260, 1792304871280, 6180666260230, 21184488791840, 72205377800600, 244837696095200

Offset: 3

Author

Alois P. Heinz, May 27 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000

Crossrefs

Column k=3 of A143396.

Programs

Maple

a:= n-> binomial(n,3)*add(Stirling2(3,j)*j^(n-3), j=0..3):
seq(a(n), n=3..40);

Formula

E.g.f.: x^3/3! * Sum_{j=0..3} Stirling2(3,j)*exp(x)^j.

a(n) = C(n,3) * Sum_{j=0..3} Stirling2(3,j) * j^(n-3).