A262253 A weighted sum over the rooted trees of n nodes (A214568).

0, 1, 3, 9, 29, 90, 285, 886, 2764, 8543, 26387, 81091, 248752, 760687, 2321950, 7072376

Offset: 0

Author

R. J. Mathar, Sep 16 2015

Keywords

• nonn
• more

Comments

(More precise name desired.)

Links

• R. Harary, R. W. Robinson, Isomorphic factorizations VIII: bisectable trees, Combinatorica 4 (2) (1984) 169-179, function F(x).
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A000107, A000081, A007098.

Formula

a(n) = sum_{k>=1} binomial(k+1,2) A214568(n,k).

A007098(x) = A(x) -A(x^2) -A000081(x)*A(x) -{A000107(x)^2 - A000107(x^2)}/2 is the relation between the generating functions, eq. prior to (4.9) by Harary-Robinson.

A(x) = A000081(x)*{A(x)-A(x^2)+ A000107(x^2)/2} +{A000081(x)+A000107(x)+A000107(x)^2}/2 , eq. (4.6) by Harary-Robinson.