OFFSET
1,5
COMMENTS
Weights are positive integer labels on the nodes. The weight of the tree is the sum of the weights of its nodes.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
F. Harary, G. Prins, The number of homeomorphically irreducible trees and other species, Acta Math. 101 (1959) 141-162, W(x,y) equation (9a)
EXAMPLE
The triangle starts
1 ;
1 1 ;
1 2 2 ;
1 3 5 4 ;
1 4 10 13 9 ;
1 5 16 31 35 20 ;
1 6 24 60 98 95 48 ;
1 7 33 103 217 304 262 115 ;
The first column (for a single node n=1) is 1, because all the weight is on that node.
PROG
(PARI)
EulerMT(u)={my(n=#u, p=x*Ser(u), vars=variables(p)); Vec(exp( sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i ))-1)}
seq(n)={my(v=[1]); for(i=2, n, v=concat([1], v + EulerMT(y*v))); v}
{my(A=seq(10)); for(n=1, #A, print(Vecrev(A[n])))} \\ Andrew Howroyd, May 19 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, May 02 2018
STATUS
approved