A274699 Number of varied unrooted labeled trees on n nodes, i.e., trees with unique vertex degree except for the leaves.

1, 1, 3, 4, 65, 126, 637, 21344, 57465, 330850, 2023901, 156312432, 502733101, 3464645380, 21505493115, 194182086016, 28828634104193, 108228186522378, 842870098110349, 5690185704481040, 49492420589959221, 521939648330427580, 151814675979620347079, 642254623640191155552, 5633344428589261601425, 40942919469553204283076, 370068971963735972601207

Offset: 1

Author

Marko Riedel, Jul 02 2016

Keywords

• nonn

Links

• Math.Stackexchange.Com, Marko R. Riedel et al., Labeled trees with a certain condition
• Marko Riedel, Maple code to compute sequence from the formula and by total enumeration

Crossrefs

Cf. A007106.

Formula

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!).