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A132433
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a(1) = 2; for n>=2, a(n) = 8*a(n-1) + 1.
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2
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2, 17, 137, 1097, 8777, 70217, 561737, 4493897, 35951177, 287609417, 2300875337, 18407002697, 147256021577, 1178048172617, 9424385380937, 75395083047497, 603160664379977, 4825285315039817, 38602282520318537, 308818260162548297, 2470546081300386377
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f.: -x*(-2+x)/(-1+x)/(-1+8*x). - R. J. Mathar, Nov 14 2007
a(n) = 9*a(n-1) - 8*a(n-2) for n>2.
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MATHEMATICA
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PROG
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(PARI) Vec(x*(2 - x) / ((1 - x)*(1 - 8*x)) + O(x^30)) \\ Colin Barker, May 12 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Vello Reeben (reeben(AT)ut.ee), Aug 25 2007
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STATUS
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approved
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