A274699 - OEIS

A274699

Number of varied unrooted labeled trees on n nodes, i.e., trees with unique vertex degree except for the leaves.

%I #21 Feb 11 2018 19:32:47

%S 1,1,3,4,65,126,637,21344,57465,330850,2023901,156312432,502733101,

%T 3464645380,21505493115,194182086016,28828634104193,108228186522378,

%U 842870098110349,5690185704481040,49492420589959221,521939648330427580,151814675979620347079,642254623640191155552,5633344428589261601425,40942919469553204283076,370068971963735972601207

%N Number of varied unrooted labeled trees on n nodes, i.e., trees with unique vertex degree except for the leaves.

%H Math.Stackexchange.Com, Marko R. Riedel et al., <a href="http://math.stackexchange.com/questions/1847086/">Labeled trees with a certain condition</a>

%H Marko Riedel, <a href="/A274699/a274699_2.maple.txt">Maple code to compute sequence from the formula and by total enumeration</a>

%F a(n) = (n-2)! Sum_{k=1..n-2} C(n,k) k! [u^k][z^{n-2}] Product_{q=1..n-2} (1 + u z^q/q!).

%Y Cf. A007106.

%K nonn

%O 1,3

%A _Marko Riedel_, Jul 02 2016