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

0,3

Comments

(More precise name desired.)

Links

Table of n, a(n) for n=0..15.

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

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.

Crossrefs

Cf. A000107, A000081, A007098.

Sequence in context: A134325 A220950 A123947 * A303546 A135142 A195624

Adjacent sequences: A262250 A262251 A262252 * A262254 A262255 A262256

Keyword

nonn,more

Author

R. J. Mathar, Sep 16 2015

Status

approved