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%I #23 Dec 22 2024 21:30:38
%S 0,211341312,67802350642790400,19045158721552047314829312,
%T 5172093060532095860985478879641600,
%U 1392436772074860374668712252110467615424512,374053097594236786223942368917529841587940071833600,100427498158122178683906767552010902133066063134008553766912,26959535297288219669523507545964171915704566051174598345329370726400
%N a(n) = (2^n)^12*((2^n)^2-1)*((2^n)^6-1)*((2^n)^8 + (2^n)^4+1).
%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 Harry J. Smith, <a href="/A064588/b064588.txt">Table of n, a(n) for n = 0..50</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (357912576, -25619989209808896, 436628173228375692804096, -1838084202651691394631840301056, 1927370980879699955817476575520096256, -503398010432197925784784284250454618013696, 32477194699655007703444278420761908023599824896, -498857322545357921467016345185865338049043131006976, 1532495540865888858358347027150309183618739122183602176).
%t Table[With[{c=2^n},c^12 (c^2-1)(c^6-1)(c^8+c^4+1)],{n,0,10}] (* _Harvey P. Dale_, Oct 23 2024 *)
%o (PARI) a(n) = { my(p=(2^n)^2); p^6*(p - 1)*(p^3 - 1)*(p^4 + p^2 + 1) } \\ _Harry J. Smith_, Sep 19 2009
%o (Python)
%o def A064588(n): return (m:=1<<(n<<1))*(m*(m*(m*(m*(m*(m*(m-1)+1)-2)+2)-2)+1)-1)+1<<12*n # _Chai Wah Wu_, Aug 20 2024
%Y Cf. A037253, A064587, A064589.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 17 2001