A016186 Expansion of 1/((1-8*x)*(1-10*x)).
1, 18, 244, 2952, 33616, 368928, 3951424, 41611392, 432891136, 4463129088, 45705032704, 465640261632, 4725122093056, 47800976744448, 482407813955584, 4859262511644672, 48874100093157376, 490992800745259008, 4927942405962072064, 49423539247696576512, 495388313981572612096, 4963106511852580896768
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..990
- Index entries for linear recurrences with constant coefficients, signature (18,-80).
Programs
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Magma
[2^n*(5^(n+1)-4^(n+1)): n in [0..40]]; // G. C. Greubel, Nov 14 2024
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Mathematica
Rest@With[{m=30}, CoefficientList[Series[Exp[9 x] Sinh[x], {x,0,m}], x]*Range[0, m]!] Table[2^n*(5^(n+1)-4^(n+1)), {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *) LinearRecurrence[{18,-80},{1,18},30] (* Harvey P. Dale, Aug 26 2019 *) -
PARI
Vec(1/((1-8*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
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SageMath
A016186=BinaryRecurrenceSequence(18,-80,1,18) print([A016186(n) for n in range(41)]) # G. C. Greubel, Nov 14 2024
Formula
From R. J. Mathar, Sep 18 2008: (Start)
a(n) = 5*10^n - 4*8^n = A081203(n+1).
Binomial transform of A081035. (End)
From Geoffrey Critzer, Jan 24 2011: (Start)
a(n) = 8*a(n-1) + 10^(n-1).
E.g.f.: exp(9*x)*sinh(x) (with offset 1). (End)
A060531(n) = a(n) - 9*a(n-1). - R. J. Mathar_, Jan 27 2011
From Vincenzo Librandi, Feb 09 2011: (Start)
a(n) = 10*a(n-1) + 8^n, a(0)=1.
a(n) = 18*a(n-1) - 80*a(n-2), a(0)=1, a(1)=18. (End)
E.g.f.: exp(9*x)*( cosh(x) + 9*sinh(x) ). - G. C. Greubel, Nov 14 2024
Extensions
More terms added by G. C. Greubel, Nov 14 2024
Comments