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Number of unlabeled unrooted trees on 2n vertices with all vertices of odd degree.
2

%I #29 Jan 20 2015 14:03:06

%S 1,1,2,3,7,13,32,74,192,497,1379,3844,11111,32500,96977,292600,894353,

%T 2758968,8590147,26947946,85138589,270646644,865260519,2780393959,

%U 8976443582,29104709339,94741504408,309529405055,1014690513653,3336805406462,11005284876792

%N Number of unlabeled unrooted trees on 2n vertices with all vertices of odd degree.

%D F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973, section 3.2.

%H StackExchange, <a href="http://math.stackexchange.com/questions/1104289/">Trees with odd degree sequence.</a>

%e When n=2 we have four vertices in the tree and the path graph does not qualify, as it contains two nodes of degree two, but the star with a center node connected to three neighboring nodes qualifies (degrees three and one are both odd).

%K nonn

%O 1,3

%A _Marko Riedel_, Jan 15 2015