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A079027 a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i)=6, m(i,j)=i/j.

%I A079027 #28 Mar 26 2024 06:05:18
%S A079027 6,35,200,1125,6250,34375,187500,1015625,5468750,29296875,156250000,
%T A079027 830078125,4394531250,23193359375,122070312500,640869140625,
%U A079027 3356933593750,17547607421875,91552734375000,476837158203125,2479553222656250,12874603271484375
%N A079027 a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i)=6, m(i,j)=i/j.
%H A079027 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-25).
%F A079027 a(n) = (n+5)*5^(n-1).
%F A079027 a(n) = 10*a(n-1)-25*a(n-2). G.f.: -x*(25*x-6) / (5*x-1)^2. - _Colin Barker_, Jun 18 2013
%F A079027 From _Amiram Eldar_, Jan 18 2021: (Start)
%F A079027 Sum_{n>=1} 1/a(n) = 15625*log(5/4) - 41837/12.
%F A079027 Sum_{n>=1} (-1)^(n+1)/a(n) = 34187/12 - 15625*log(6/5). (End)
%p A079027 A079027:=n->(n + 5)*5^(n - 1); seq(A079027(n), n=1..50); # _Wesley Ivan Hurt_, Nov 30 2013
%t A079027 Table[(n + 5)*5^(n - 1), {n, 50}] (* _Wesley Ivan Hurt_, Nov 30 2013 *)
%t A079027 LinearRecurrence[{10,-25},{6,35},30] (* _Harvey P. Dale_, Jun 14 2022 *)
%o A079027 (PARI) a(n) = matdet(matrix(n, n, i, j, if(i==j, 6, i/j))); \\ _Michel Marcus_, Nov 30 2013
%Y A079027 Cf. A006234.
%K A079027 nonn,easy
%O A079027 1,1
%A A079027 _Benoit Cloitre_, Feb 01 2003
%E A079027 More terms from _Michel Marcus_, Nov 30 2013