login
a(n) = n^12*(n^8+n^4+1)*(n^6-1)*(n^2-1).
5

%I #18 Aug 21 2024 10:12:40

%S 0,0,211341312,20560831566912,67802350642790400,35817806390625000000,

%T 5974842736157763686400,450782974156649555296512,

%U 19045158721552047314829312,516964372056378442547769600,9900980198009901000000000000

%N a(n) = n^12*(n^8+n^4+1)*(n^6-1)*(n^2-1).

%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 Vincenzo Librandi, <a href="/A037253/b037253.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (29, -406, 3654, -23751, 118755, -475020, 1560780, -4292145, 10015005, -20030010, 34597290, -51895935, 67863915, -77558760, 77558760, -67863915, 51895935, -34597290, 20030010, -10015005, 4292145, -1560780, 475020, -118755, 23751, -3654, 406, -29, 1).

%t Table[n^12(n^8+n^4+1)(n^6-1)(n^2-1),{n,0,20}] (* _Harvey P. Dale_, Sep 15 2011 *)

%o (Magma) [n^12*(n^8+n^4+1)*(n^6-1)*(n^2-1) :n in [0..15]]; // Sep 15 2011

%o (Python)

%o def A037253(n): return (m:=n**2)**6*(m*(m*(m*(m*(m*(m*(m*(m-1)+1)-2)+2)-2)+1)-1)+1) # _Chai Wah Wu_, Aug 20 2024

%Y Cf. A064587, A064588, A064589.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_.