A160705 Hankel transform of A052702.

0, 0, 0, 0, 1, 1, -1, -4, -4, 5, 9, 9, -14, -16, -16, 30, 25, 25, -55, -36, -36, 91, 49, 49, -140, -64, -64, 204, 81, 81, -285, -100, -100, 385, 121, 121, -506, -144, -144, 650, 169, 169, -819, -196, -196, 1015, 225, 225, -1240, -256, -256

Offset: 0

Author

Paul Barry, May 24 2009

Keywords

• easy
• sign

Comments

a(n+5) is the Hankel transform of A052702(n+4).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,-4,0,0,-6,0,0,-4,0,0,-1).

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); [0,0,0,0] cat Coefficients(R!(x^4*(1-x)*(1+x+x^2)*(x^4+x^3-x^2+x+1)/( (1+x)^4*(x^2-x+1)^4 ))); // G. C. Greubel, May 02 2018

Mathematica

LinearRecurrence[{0,0,-4,0,0,-6,0,0,-4,0,0,-1}, {0,0,0,0,1,1,-1,-4,-4,5,9,9}, 50] (* G. C. Greubel, May 02 2018 *)

PARI

x='x+O('x^50); concat([0,0,0,0], Vec(x^4*(1-x)*(1+x+x^2)*(x^4+x^3-x^2+x+1)/( (1+x)^4*(x^2-x+1)^4 ))) \\ G. C. Greubel, May 02 2018

Formula

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

a(n) = -4*a(n-3) -6*a(n-6) -4*a(n-9) -a(n-12).