A356186 Number of labeled trees on [2n] with a bicentroid.

0, 1, 12, 810, 143360, 49218750, 27935373312, 23751648836916, 28301429298954240, 45046920790988254710, 92378000000000000000000, 237289687212632836205339916, 746430126201849206626773368832, 2822726846177838977566127355808300

Offset

0,3

Comments

This sequence is the labeled version of A102911 where the pertinent definitions can be found.

Links

Table of n, a(n) for n=0..13.

N. J. A. Sloane, Illustration of initial terms

Formula

a(n) = binomial(2n,n)*n^(2n-2)/2 = A000984(n)*A000169(n)^2/2.

Example

a(3) = 810.  In the illustrations by Sloane found in the link above, for n = 6, there are A102911(3) = 3 trees with a bicentroid: the first, second and last trees shown.  They have 360, 360, and 90 labelings respectively.  360 + 360 + 90 = 810.

Mathematica

Prepend[Table[Binomial[2 n, n] n^(n - 1) n^(n - 1)/2, {n, 1, 12}], 0]

Crossrefs

Cf. A102911, A000984, A000169.

Sequence in context: A178023 A305935 A228182 * A003748 A280333 A350412

Adjacent sequences: A356183 A356184 A356185 * A356187 A356188 A356189

Keyword

nonn

Author

Geoffrey Critzer, Jul 31 2022

Status

approved