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%I #19 Oct 14 2023 12:11:42
%S 4,15,72,420,2880,22680,201600,1995840,21772800,259459200,3353011200,
%T 46702656000,697426329600,11115232128000,188305108992000,
%U 3379030566912000,64023737057280000,1277273554292736000,26761922089943040000,587545834974658560000,13488008733331292160000
%N a(n) = (n+1)*(n-1)!/2.
%C 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
%F a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(j+1)^(n+1)/(n+1). - _Vladimir Kruchinin_, Jun 01 2013
%F D-finite with recurrence -n*a(n) +(n-1)*(n+1)*a(n-1) = 0. - _R. J. Mathar_, Feb 01 2022
%e For n >= 1, the sequence is 1, 3/2, 4, 15, 72, 420, 2880, 22680, 201600, 1995840, ...
%t Table[((n+1)*(n-1)!)/2,{n,3,30}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2011 *)
%t 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 *)
%Y Equals A001048/2.
%K nonn,easy
%O 3,1
%A _N. J. A. Sloane_, Sep 02 2010
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