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%I #22 Mar 15 2024 02:18:53
%S 2,17,137,1097,8777,70217,561737,4493897,35951177,287609417,
%T 2300875337,18407002697,147256021577,1178048172617,9424385380937,
%U 75395083047497,603160664379977,4825285315039817,38602282520318537,308818260162548297,2470546081300386377
%N a(1) = 2; for n>=2, a(n) = 8*a(n-1) + 1.
%C Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=7, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=(-1)^n*charpoly(A,-1). - _Milan Janjic_, Feb 21 2010
%D V. Reeben, The highly composite numbers by Srinivasa Ramanujan and the fundamental constants of physics. J. Madras Univ., Sect. B, 51 (Ramanujan's 100th birthday issue, with a Table of h.c.n.'s up to 10^102), (1988) 88-146.
%H Colin Barker, <a href="/A132433/b132433.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F G.f.: -x*(-2+x)/(-1+x)/(-1+8*x). - _R. J. Mathar_, Nov 14 2007
%F a(n) = 9*a(n-1) - 8*a(n-2) for n>2.
%t NestList[8#+1&,2,20] (* _Harvey P. Dale_, Aug 30 2021 *)
%o (PARI) Vec(x*(2 - x) / ((1 - x)*(1 - 8*x)) + O(x^30)) \\ _Colin Barker_, May 12 2017
%Y Cf. A132434.
%K nonn,easy
%O 1,1
%A Vello Reeben (reeben(AT)ut.ee), Aug 25 2007
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