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

1,2

Comments

Essentially the same as A005025. - R. J. Mathar, Aug 02 2008

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).

Formula

G.f.: x/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).

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}]

Prog

(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
(Sage)
def A122588_list(prec):
    P.<x> = 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

Crossrefs

Cf. A005021, A005025, A094256, A122589.

Sequence in context: A055854 A202514 A005025 * A277999 A295203 A334977

Adjacent sequences: A122585 A122586 A122587 * A122589 A122590 A122591

Keyword

nonn,easy,less

Author

Roger L. Bagula and Gary W. Adamson, Sep 19 2006

Extensions

Generating function corrected by R. J. Mathar, Jul 09 2009

New name (using g.f.) and editing by Joerg Arndt, Feb 12 2015

Status

approved