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%I #18 Sep 08 2022 08:44:52
%S 4,200,3360,43680,551040,7136640,96768000,1383782400,20916403200,
%T 334183449600,5637529497600,100255034880000,1876076826624000,
%U 36872930045952000,759748346413056000,16381540188389376000,368990137906790400000,8668429855133368320000,212061470640708648960000
%N a(n) = n!*(3*n^2 - 15*n + 10)/6, n > 4.
%H G. C. Greubel, <a href="/A034862/b034862.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.
%F (3*n^2-21*n+28)*a(n) - n*(3*n^2-15*n+10)*a(n-1) = 0. - _R. J. Mathar_, Apr 03 2017
%F E.g.f.: x^4*(1 +7*x +x^2 -3*x^3)/(6*(1-x)^3). - _G. C. Greubel_, Feb 22 2018
%F a(n) = A034861(n), n>=5. - _R. J. Mathar_, Apr 14 2018
%t Join[{4}, Table[n!*(3*n^2 -15*n +10)/6, {n,5,30}]] (* or *) Drop[With[ {nn=50}, CoefficientList[ Series[x^4*(1+7*x+x^2-3*x^3)/(6*(1-x)^3), {x, 0, nn}], x]*Range[0, nn]!],4] (* _G. C. Greubel_, Feb 22 2018 *)
%o (PARI) for(n=4,30, print1(if(n==4, 4, n!*(3*n^2 -15*n +10)/6), ", ")) \\ _G. C. Greubel_, Feb 22 2018
%o (Magma) [4] cat [Factorial(n)*(3*n^2 -15*n +10)/6: n in [5..30]]; // _G. C. Greubel_, Feb 22 2018
%K nonn,easy
%O 4,1
%A _N. J. A. Sloane_
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