A358732 Number of labeled trees covering 2n nodes, half of which are leaves.

0, 12, 720, 109200, 31752000, 15186346560, 10852244282880, 10851787634688000, 14481281691676800000, 24881574582258352358400, 53525038934303849706393600, 140958354488116955062668595200, 446153762528143389466306560000000, 1671353230826683972965623004979200000

Offset: 1

Author

Gus Wiseman, Dec 01 2022

Keywords

• nonn

Examples

			The a(2) = 12 trees:
  {{1,2},{1,3},{2,4}}
  {{1,2},{1,3},{3,4}}
  {{1,2},{1,4},{2,3}}
  {{1,2},{1,4},{3,4}}
  {{1,2},{2,3},{3,4}}
  {{1,2},{2,4},{3,4}}
  {{1,3},{1,4},{2,3}}
  {{1,3},{1,4},{2,4}}
  {{1,3},{2,3},{2,4}}
  {{1,3},{2,4},{3,4}}
  {{1,4},{2,3},{2,4}}
  {{1,4},{2,3},{3,4}}
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

A central column of A055314.

The unlabeled rooted version is A185650.

The unlabeled version is A358107.

A000272 counts trees, bisection A163395.

A001187 counts connected graphs.

A006129 counts covering graphs.

A014068 counts graphs with n vertices and n-1 edges.

Cf. A000055, A001349, A006125.

Programs

Mathematica

a[n_]:=StirlingS2[2*n-2, n]*(2*n)!/n!; Array[a,14] (* Stefano Spezia, Aug 02 2024 *)

PARI

a(n) = stirling(2*n-2, n, 2)*(2*n)!/n! \\ Andrew Howroyd, Dec 30 2022

Formula

a(n) = A055314(2*n, n) = Stirling2(2*n-2, n)*(2*n)!/n!. - Andrew Howroyd, Dec 30 2022

Extensions

Terms a(6) and beyond from Andrew Howroyd, Dec 30 2022