A356259 Number of labeled rooted trees on [n] that have a primary branch.
0, 2, 6, 60, 500, 7290, 100842, 1978368, 38263752, 949218750, 23579476910, 709026379776, 21505924728444, 760772509715764, 27246730957031250, 1109165339867873280, 45798768824157052688, 2109518949433090534902
Offset: 1
Keywords
Examples
a(5) = 500. In the illustrations by Sloane found in the link above, for n = 5, there are A027415(5) = 6 rooted trees with a primary branch: the first six trees shown.
Links
- N. J. A. Sloane, Illustration of initial terms
Programs
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Mathematica
Table[Sum[Binomial[n, n - i] (n - i)^(n - i - 1)*i^(i - 1), {i, 1,Floor[n/2]}], {n, 1, 20}]
Comments