A358732 - OEIS

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

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OFFSET

1,2

LINKS

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

FORMULA

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

EXAMPLE

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}}

MATHEMATICA

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

PROG

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

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.

Sequence in context: A141421 A000909 A375105 * A162447 A061025 A042749

Adjacent sequences: A358729 A358730 A358731 * A358733 A358734 A358735

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 01 2022

EXTENSIONS

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

STATUS

approved