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a(n) = n^2*(n^2 + 1)*(n-1).
3

%I #23 Jun 14 2024 22:31:09

%S 0,0,20,180,816,2600,6660,14700,29120,53136,90900,147620,229680,

%T 344760,501956,711900,986880,1340960,1790100,2352276,3047600,3898440,

%U 4929540,6168140,7644096,9390000,11441300

%N a(n) = n^2*(n^2 + 1)*(n-1).

%C Conjecture: satisfies a linear recurrence having signature (6, -15, 20, -15, 6, -1). - _Harvey P. Dale_, Jul 27 2019

%C This conjecture is true since for any series a(n) = P(n) (P polynomial in n of degree d) there is an o.g.f. Q(x)/(1-x)^(d+1). - _Georg Fischer_, Feb 17 2021

%D R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14.

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

%H Vincenzo Librandi, <a href="/A037250/b037250.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%p seq(coeff(series(4*x^2*(x^3+9*x^2+15*x+5)/(x-1)^6, x, n+1),x,n), n = 0..30); # _Georg Fischer_, Feb 17 2021

%t Table[n^2 (n^2+1)(n-1),{n,0,30}] (* _Harvey P. Dale_, Jul 27 2019 *)

%o (Magma) [n^2*(n^2+1)*(n-1): n in [0..30]]; // _Vincenzo Librandi_, Sep 14 2011

%Y Cf. A064487, A064583.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_