A171005 a(n) = (n+1)*(n-1)!/2.

4, 15, 72, 420, 2880, 22680, 201600, 1995840, 21772800, 259459200, 3353011200, 46702656000, 697426329600, 11115232128000, 188305108992000, 3379030566912000, 64023737057280000, 1277273554292736000, 26761922089943040000, 587545834974658560000, 13488008733331292160000

Offset

3,1

Comments

A wheel graph is a graph with n+1 vertices (n>=3) formed by connecting a single vertex to all vertices of an n-cycle. a(n) is the number of labeled wheel graphs. - Geoffrey Critzer, Feb 02 2014

Links

Table of n, a(n) for n=3..23.

Formula

a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(j+1)^(n+1)/(n+1). - Vladimir Kruchinin, Jun 01 2013

D-finite with recurrence -n*a(n) +(n-1)*(n+1)*a(n-1) = 0. - R. J. Mathar, Feb 01 2022

Example

For n >= 1, the sequence is 1, 3/2, 4, 15, 72, 420, 2880, 22680, 201600, 1995840, ...

Mathematica

Table[((n+1)*(n-1)!)/2, {n, 3, 30}] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2011 *)
nn=20; Drop[Range[0, nn]!CoefficientList[Series[x (Log[1/(1-x)]/2+x^2/4+x/2), {x, 0, nn}], x], 4] (* Geoffrey Critzer, Feb 02 2014 *)

Crossrefs

Equals A001048/2.

Sequence in context: A278640 A026992 A039764 * A303229 A340355 A356009

Adjacent sequences: A171002 A171003 A171004 * A171006 A171007 A171008

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 02 2010

Status

approved