A160706 Hankel transform of A052702(n+1).

0, 0, 0, 1, 0, -1, -2, 0, 2, 3, 0, -3, -4, 0, 4, 5, 0, -5, -6, 0, 6, 7, 0, -7, -8, 0, 8, 9, 0, -9, -10, 0, 10, 11, 0, -11, -12, 0, 12, 13, 0, -13, -14, 0, 14, 15, 0, -15, -16, 0, 16, 17, 0, -17, -18, 0, 18, 19, 0, -19, -20

Offset: 0

Author

Paul Barry, May 24 2009

Keywords

• easy
• sign

Comments

a(n+5) is the Hankel transform of A052702(n+3).

Links

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

Programs

Magma

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

Mathematica

LinearRecurrence[{1, -1, -1, 1, -1}, {0, 0, 0, 1, 0}, 100] (* G. C. Greubel, May 02 2018 *)

PARI

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

Formula

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