A064583 a(n) = n^4*(n^4+1)*(n^2-1).

0, 0, 816, 53136, 986880, 9390000, 58831920, 276825696, 1057222656, 3444262560, 9900990000, 25724822640, 61490347776, 137047559376, 287786357040, 574098840000, 1095233372160, 2009042197056, 3559481173296, 6114129610320, 10214463840000, 16642143690480, 26505160063536

Offset: 0

Author

N. J. A. Sloane, Oct 17 2001

Keywords

• nonn

References

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

Links

• Harry J. Smith, Table of n, a(n) for n=0,...,500
• Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Crossrefs

Cf. A064487, A037250.

Programs

Magma

[n^4*(n^4+1)*(n^2-1): n in [0..25]]; // Vincenzo Librandi, Jun 20 2018

Mathematica

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 *)
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 *)

PARI

a(n) = { n^4*(n^4 + 1)*(n^2 - 1) } \\ Harry J. Smith, Sep 18 2009

Formula

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

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