A262253 - OEIS

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

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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