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A034863 a(n) = n!*(4*n^3 - 30*n^2 + 40*n + 3)/24. 2

%I #19 Sep 08 2022 08:44:52

%S -61,-235,810,38850,757680,12836880,212133600,3554258400,61372080000,

%T 1100366467200,20555914579200,400638734496000,8148554878464000,

%U 172878910364160000,3823017399032832000,88035572875041792000,2108819186504110080000

%N a(n) = n!*(4*n^3 - 30*n^2 + 40*n + 3)/24.

%H G. C. Greubel, <a href="/A034863/b034863.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 Conjecture: (-96*n + 27161)*a(n) + (96*n^2 - 99580*n + 199917)*a(n-1) +(72707*n - 61983)*(n-1)*a(n-2) = 0. - _R. J. Mathar_, Apr 03 2017

%F E.g.f.: x^4*(-61 + 197*x - 151*x^2 + 39*x^3)/(24*(1-x)^4). - _G. C. Greubel_, Feb 16 2018

%p [seq(factorial(n)*(4*n^3-30*n^2+40*n+3)/24,n=4..22)]; # _Muniru A Asiru_, Feb 17 2018

%t Table[n!(4n^3-30n^2+40n+3)/24,{n,4,20}] (* _Harvey P. Dale_, Apr 14 2015 *)

%o (PARI) for(n=4,30, print1(n!*(4*n^3-30*n^2+40*n+3)/24, ", ")) \\ _G. C. Greubel_, Feb 16 2018

%o (Magma) [Factorial(n)*(4*n^3-30*n^2+40*n+3)/24: n in [4..30]]; // _G. C. Greubel_, Feb 16 2018

%o (GAP) A034863:=List([4..22],n->Factorial(n)*(4*n^3-30*n^2+40*n+3)/24); # _Muniru A Asiru_, Feb 17 2018

%K sign

%O 4,1

%A _N. J. A. Sloane_

%E More terms from _Harvey P. Dale_, Apr 14 2015

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)