This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108982 #22 Feb 24 2024 01:12:02
%S A108982 1,6,29,146,729,3646,18229,91146,455729,2278646,11393229,56966146,
%T A108982 284830729,1424153646,7120768229,35603841146,178019205729,
%U A108982 890096028646,4450480143229,22252400716146,111262003580729,556310017903646
%N A108982 Inverse binomial of A003949.
%C A108982 Let A be the Hessenberg matrix of order n, defined by: A[1,j] = 1, A[i,i] = -3, A[i,i-1] = -1, and A[i,j] = 0 otherwise. Then, for n>=1, a(n-1) = charpoly(A,2). - _Milan Janjic_, Jan 27 2010
%H A108982 G. C. Greubel, <a href="/A108982/b108982.txt">Table of n, a(n) for n = 0..1000</a>
%H A108982 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, 5).
%F A108982 a(n) = 4*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 6.
%F A108982 a(2n) = 5*a(2n-1) - 1 and a(2n+1) = 5*a(2n) + 1.
%F A108982 From _G. C. Greubel_, Sep 25 2019: (Start)
%F A108982 G.f.: (1 + 2*x)/((1+x)*(1-5*x)).
%F A108982 E.g.f.: (7*exp(5*x) - exp(-x))/6. (End)
%p A108982 seq((7*5^n - (-1)^n)/6, n=0..25); # _G. C. Greubel_, Sep 25 2019
%t A108982 LinearRecurrence[{4,5},{1,6},30] (* _Harvey P. Dale_, Jul 07 2013 *)
%o A108982 (PARI) vector(26, n, (7*5^(n-1) + (-1)^n)/6) \\ _G. C. Greubel_, Sep 25 2019
%o A108982 (Magma) [(7*5^n - (-1)^n)/6: n in [0..25]]; // _G. C. Greubel_, Sep 25 2019
%o A108982 (Sage) [(7*5^n - (-1)^n)/6 for n in (0..25)] # _G. C. Greubel_, Sep 25 2019
%o A108982 (GAP) List([0..25], n-> (7*5^n - (-1)^n)/6); # _G. C. Greubel_, Sep 25 2019
%K A108982 nonn
%O A108982 0,2
%A A108982 _Philippe Deléham_, Jul 23 2005
%E A108982 Corrected and extended by _T. D. Noe_, Nov 07 2006