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

1,3

Links

Table of n, a(n) for n=1..27.

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

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!).

Crossrefs

Cf. A007106.

Sequence in context: A349587 A278035 A079076 * A060356 A052323 A356292

Adjacent sequences: A274696 A274697 A274698 * A274700 A274701 A274702

Keyword

nonn

Author

Marko Riedel, Jul 02 2016

Status

approved