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

0,8

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).

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).

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 *)

Prog

(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
(Magma) m:=50; R<x>:=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

Crossrefs

Sequence in context: A214070 A096641 A155693 * A107851 A302337 A098821

Adjacent sequences: A160702 A160703 A160704 * A160706 A160707 A160708

Keyword

easy,sign

Author

Paul Barry, May 24 2009

Status

approved