OFFSET
0,3
COMMENTS
With offset = 3, a(n) is the number of forests having exactly three rooted plane trees with n total nodes. - Geoffrey Critzer, Feb 22 2013
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
Plug g.f. for A000108, 1/2*(1-(1-4*x)^(1/2))/x, into cycle index for dihedral group D_6.
Cycle index for D_6: 1/6*Z[1]^3+1/2*Z[1]*Z[2]+1/3*Z[3].
a(n) = Sum_{j=0..3} A275431(n,j). - Alois P. Heinz, Sep 20 2017
MATHEMATICA
nn=30; Drop[CoefficientList[Series[ CycleIndex[SymmetricGroup[3], s]/.Table[s[i]->(1-(1-4x^i)^(1/2))/2, {i, 1, nn}], {x, 0, nn}], x], 3] (* Geoffrey Critzer, Feb 22 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 19 2001
STATUS
approved