A038094 Number of rooted graphs on n labeled nodes where the root has degree 2.

6, 96, 1920, 61440, 3440640, 352321536, 67645734912, 24739011624960, 17416264183971840, 23779006032516218880, 63309225660971181146112, 330036748754793764694786048, 3379576307249088150474609131520

Offset: 3

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..80

Crossrefs

Cf. A006125, A038095, A038096, A038097, A103904.

Programs

Magma

[n*Binomial(n-1, 2)*2^Binomial(n-1, 2): n in [3..20]]; // Vincenzo Librandi, Mar 29 2014

Mathematica

Table[n*Binomial[n-1, 2]*2^Binomial[n-1, 2], {n, 3, 20}] (* Vaclav Kotesovec, Mar 29 2014 *)

PARI

a(n) = {n * binomial(n-1, 2) * 2^binomial(n-1, 2)} \\ Andrew Howroyd, Nov 23 2020

Formula

a(n) = n * binomial(n-1, 2) * 2^binomial(n-1, 2).

a(n) = n * A103904(n-1) for n >= 3. - Andrew Howroyd, Nov 23 2020