A176290 Hankel transform of A105872.

1, 2, -3, -75, -650, -4507, -28267, -167406, -955271, -5310911, -28962586, -155616567, -826329687, -4345964510, -22675946635, -117526104883, -605643805098, -3105646720979, -15856669574339, -80653146223054

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 (10,-27,10,-1).

Crossrefs

Cf. A105872.

Programs

GAP

a:=[1,2,-3,-75];; for n in [5..30] do a[n]:=10*a[n-1]-27*a[n-2]+10*a[n-3] -a[n-4]; od; a; # G. C. Greubel, Nov 25 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2 )); // G. C. Greubel, Nov 25 2019

Maple

seq(coeff(series((1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2, x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 25 2019

Mathematica

LinearRecurrence[{10,-27,10,-1},{1,2,-3,-75},30] (* Harvey P. Dale, Oct 29 2017 *)

PARI

my(x='x+O('x^30)); Vec((1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2) \\ G. C. Greubel, Nov 25 2019

Sage

def A176290_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2).list()
A176290_list(30) # G. C. Greubel, Nov 25 2019

Formula

G.f.: (1-8*x+4*x^2-x^3)/(1-5*x+x^2)^2.