%I #8 Sep 16 2015 12:22:20

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

%T 7072376

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

%C (More precise name desired.)

%H R. Harary, R. W. Robinson, <a href="http://dx.doi.org/10.1007/BF02579217">Isomorphic factorizations VIII: bisectable trees</a>, Combinatorica 4 (2) (1984) 169-179, function F(x).

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

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

%F 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.

%F 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.

%Y Cf. A000107, A000081, A007098.

%K nonn,more

%O 0,3

%A _R. J. Mathar_, Sep 16 2015