A176288 Hankel transform of A176287.

1, 3, 15, 55, 131, 163, -169, -1521, -4437, -7429, -2945, 26471, 101587, 207699, 201639, -306497, -1907461, -4718165, -6464305, 547863, 30463779, 93816323, 161591287, 97035119, -400669877, -1676486565, -3504149217, -3693262649

Offset: 0

Author

Paul Barry, Apr 14 2010

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-17,24,-16).

Programs

GAP

a:=[1,3,15,55];; for n in [5..30] do a[n]:=6*a[n-1]-17*a[n-2]+24*a[n-3] -16*a[n-4]; od; a; # G. C. Greubel, Nov 25 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2 )); // G. C. Greubel, Nov 25 2019

Maple

seq(coeff(series((1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2, x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 25 2019

Mathematica

LinearRecurrence[{6,-17,24,-16},{1,3,15,55},30] (* Harvey P. Dale, Jun 12 2017 *)

PARI

my(x='x+O('x^30)); Vec((1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2) \\ G. C. Greubel, Nov 25 2019

Sage

def A176288_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2 ).list()
A176288_list(30) # G. C. Greubel, Nov 25 2019

Formula

G.f.: (1-3*x+14*x^2-8*x^3)/(1-3*x+4*x^2)^2.

a(n) = 2^n*( (2n+7)*sin(2n*atan(1/sqrt(7)))/sqrt(7) - (2*n-1)*cos(2n*atan(1/sqrt(7)))).