A122588 Expansion of x/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).
1, 9, 53, 260, 1156, 4845, 19551, 76912, 297275, 1134705, 4292145, 16128061, 60304951, 224660626, 834641671, 3094322026, 11453607152, 42344301686, 156404021389, 577291806894, 2129654436910, 7853149169635, 28949515515376, 106692395098433, 393137817645838
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- MathPuzzle, Chebyshev Polynomials.
- Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1).
Programs
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Magma
I:=[1,9,53,260,1156]; [n le 5 select I[n] else 9*Self(n-1) -28*Self(n-2) +35*Self(n-3) -15*Self(n-4) +Self(n-5): n in [1..30]]; // G. C. Greubel, Nov 29 2021
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Mathematica
m = 10; p[x_]:= ExpandAll[x^m*ChebyshevU[m, 1/x]]; Table[SeriesCoefficient[ Series[2^(n+m-1)*x/p[x], {x,0,30}], n], {n,1,30,2}] -
Sage
def A122588_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( x/(1-9*x+28*x^2-35*x^3+15*x^4-x^5) ).list() a=A122588_list(31); a[1:] # G. C. Greubel, Nov 29 2021
Formula
G.f.: x/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).
Extensions
Generating function corrected by R. J. Mathar, Jul 09 2009
New name (using g.f.) and editing by Joerg Arndt, Feb 12 2015
Comments