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%I #24 Sep 08 2022 08:44:52
%S 4,60,720,7560,80640,907200,10886400,139708800,1916006400,28021593600,
%T 435891456000,7192209024000,125536739328000,2311968282624000,
%U 44816615940096000,912338253066240000
%N a(n) = n!*(n-4)/2, n > 4, and a(4) = 4.
%H G. C. Greubel, <a href="/A034866/b034866.txt">Table of n, a(n) for n = 4..445</a>
%H J. Riordan, <a href="http://dx.doi.org/10.1147/rd.45.0473">Enumeration of trees by height and diameter</a>, IBM J. Res. Dev. 4 (1960), 473-478.
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F a(n) = A034865(n), n > 4. - _R. J. Mathar_, Oct 20 2008
%F (-n+5)*a(n) + n*(n-4)*a(n-1) = 0. - _R. J. Mathar_, Apr 03 2017
%F E.g.f.: x^4*(1 + x + x^2)/(6*(1 - x)^2). - _G. C. Greubel_, Feb 16 2018
%p [4,seq(factorial(n)*(n-4)/2,n=5..20)]; # _Muniru A Asiru_, Feb 17 2018
%t Join[{4}, Table[n!*(n-4)/2, {n,5,30}]] (* or *) Drop[With[{nn = 30}, CoefficientList[Series[x^4*(1 + x + x^2)/(6*(1 - x)^2), {x, 0, nn}], x]*Range[0, nn]!], 4] (* _G. C. Greubel_, Feb 16 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(x^4*(1+x+x^2)/(6*(1-x)^2))) \\ _G. C. Greubel_, Feb 16 2018
%o (Magma) [4] cat [Factorial(n)*(n-4)/2: n in [5..30]]; // _G. C. Greubel_, Feb 16 2018
%o (GAP) A034866:=Concatenation([4],List([5..20],n->Factorial(n)*(n-4)/2)); # _Muniru A Asiru_, Feb 17 2018
%K nonn,easy
%O 4,1
%A _N. J. A. Sloane_
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