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.
6, 35, 200, 1125, 6250, 34375, 187500, 1015625, 5468750, 29296875, 156250000, 830078125, 4394531250, 23193359375, 122070312500, 640869140625, 3356933593750, 17547607421875, 91552734375000, 476837158203125, 2479553222656250, 12874603271484375
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (10,-25).
Crossrefs
Cf. A006234.
Programs
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Maple
A079027:=n->(n + 5)*5^(n - 1); seq(A079027(n), n=1..50); # Wesley Ivan Hurt, Nov 30 2013
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Mathematica
Table[(n + 5)*5^(n - 1), {n, 50}] (* Wesley Ivan Hurt, Nov 30 2013 *) LinearRecurrence[{10,-25},{6,35},30] (* Harvey P. Dale, Jun 14 2022 *) -
PARI
a(n) = matdet(matrix(n, n, i, j, if(i==j, 6, i/j))); \\ Michel Marcus, Nov 30 2013
Formula
a(n) = (n+5)*5^(n-1).
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
From Amiram Eldar, Jan 18 2021: (Start)
Sum_{n>=1} 1/a(n) = 15625*log(5/4) - 41837/12.
Sum_{n>=1} (-1)^(n+1)/a(n) = 34187/12 - 15625*log(6/5). (End)
Extensions
More terms from Michel Marcus, Nov 30 2013