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%I #17 May 24 2021 15:21:27
%S 0,9,98,516,1870,5369,13132,28560,56772,105105,183678,306020,489762,
%T 757393,1137080,1663552,2379048,3334329,4589754,6216420,8297366,
%U 10928841,14221636,18302480,23315500,29423745,36810774,45682308,56267946,68822945,83630064
%N a(n) = n*(n+1)^2*(2+n)*(3+2*n)*(19+8*n)/180.
%C Let M_n be the n X n matrix M_(i,j) = i^2-j^2. Then the characteristic polynomial of M_n is x^n+a(n-1)x^(n-2). - _Benoit Cloitre_, Nov 30 2002
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: -x*(x^3+19*x^2+35*x+9)/(x-1)^7. [_Colin Barker_, Oct 22 2012]
%F a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - _Wesley Ivan Hurt_, May 24 2021
%t Table[n (n+1)^2(2+n)(3+2n)(19+8n)/180,{n,0,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{0,9,98,516,1870,5369,13132},40] (* _Harvey P. Dale_, Dec 19 2017 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 14 2002
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