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%I #16 Sep 08 2022 08:45:04
%S 0,0,816,53136,986880,9390000,58831920,276825696,1057222656,
%T 3444262560,9900990000,25724822640,61490347776,137047559376,
%U 287786357040,574098840000,1095233372160,2009042197056,3559481173296,6114129610320,10214463840000,16642143690480,26505160063536
%N a(n) = n^4*(n^4+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, p. xvi.
%H Harry J. Smith, <a href="/A064583/b064583.txt">Table of n, a(n) for n=0,...,500</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
%F a(0)=0, a(1)=0, a(2)=816, a(3)=53136, a(4)=986880, a(5)=9390000, a(6)=58831920, a(7)=276825696, a(8)=1057222656, a(9)=3444262560, a(10)=9900990000, a(n)= 11*a(n-1)- 55*a(n-2)+ 165*a(n-3)- 330*a(n-4)+ 462*a(n-5)- 462*a(n-6)+ 330*a(n-7)- 165*a(n-8)+ 55*a(n-9)- 11*a(n-10)+ a(n-11). - _Harvey P. Dale_, Aug 17 2015
%F G.f.: 48*x^2*(17 + 920*x + 9318*x^2 + 27545*x^3 + 27545*x^4 + 9318*x^5 + 920*x^6 + 17*x^7)/(1-x)^11. - _Vincenzo Librandi_, Jun 20 2018
%t Table[n^4 (n^4+1)(n^2-1),{n,0,30}] (* or *) LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,0,816,53136,986880,9390000,58831920,276825696,1057222656,3444262560,9900990000},30] (* _Harvey P. Dale_, Aug 17 2015 *)
%t CoefficientList[Series[48 x^2 (17 + 920 x + 9318 x^2 + 27545 x^3 + 27545 x^4 + 9318 x^5 + 920 x^6 + 17 x^7)/(1 - x)^11, {x, 0, 33}], x] (* _Vincenzo Librandi_, Jun 20 2018 *)
%o (PARI) { for (n=0, 500, write("b064583.txt", n, " ", n^4*(n^4 + 1)*(n^2 - 1)) ) } \\ _Harry J. Smith_, Sep 18 2009
%o (Magma) [n^4*(n^4+1)*(n^2-1): n in [0..25]]; // _Vincenzo Librandi_, Jun 20 2018
%Y Cf. A064487, A037250.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Oct 17 2001
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