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%I #27 Sep 08 2022 08:44:52
%S 3,36,300,2520,22680,221760,2358720,27216000,339292800,4550515200,
%T 65383718400,1002550348800,16345929600000,282457663488000,
%U 5157467707392000,99236792438784000,2007144156745728000,42575785143091200000,945182430176624640000,21918014191663349760000
%N a(n) = n!*(2*n-5)/2.
%H Vincenzo Librandi, <a href="/A034860/b034860.txt">Table of n, a(n) for n = 3..200</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 (-2*n+7)*a(n) + n*(2*n-5)*a(n-1) = 0. - _R. J. Mathar_, Apr 03 2017
%F E.g.f.: x^3*(1 + x)/(2*(1 - x)^2). - _Ilya Gutkovskiy_, May 23 2017
%t Table[n!*(2*n-5)/2,{n,3,20}] (* _Harvey P. Dale_, Oct 10 2012 *)
%o (Magma) [Factorial(n)*(2*n-5)/2: n in [3..22]]; // _Vincenzo Librandi_, May 25 2017
%o (PARI) for(n=3,30, print1(n!*(2*n-5)/2, ", ")) \\ _G. C. Greubel_, Feb 16 2018
%K nonn,easy
%O 3,1
%A _N. J. A. Sloane_