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%I #17 Feb 23 2021 05:26:11
%S 1,5778,40169,87727,136338,184958,233578,282198,330818,379438,428058,
%T 476678,525298,573918,622538,671158,719778,768398,817018,865638,
%U 914258,962878,1011498,1060118,1108738,1157358,1205978,1254598,1303218,1351838
%N Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-9).
%C More generally for any n>=floor((m+1)/2) the trace of M(n)^(-m) = binomial(2*m,m)*n-2^(2*m-1)+binomial(2*m-1,m).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 48620n-106762, with n>4, a(1)=1, a(2)=5778, a(3)=40169, a(4)=87727.
%F From _Colin Barker_, Mar 18 2012: (Start)
%F a(n) = 2*a(n-1)-a(n-2) for n>6.
%F G.f.: x*(1+5776*x+28614*x^2+13167*x^3+1053*x^4+9*x^5)/(1-x)^2. (End)
%t Rest@ CoefficientList[Series[x (1 + 5776 x + 28614 x^2 + 13167 x^3 + 1053 x^4 + 9 x^5)/(1 - x)^2, {x, 0, 30}], x] (* _Michael De Vlieger_, Feb 22 2021 *)
%Y Cf. A114358, A114359, A114360.
%K nonn,easy
%O 1,2
%A _Benoit Cloitre_, Feb 09 2006
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