A145063 - OEIS

A145063

Hankel transform of A145062.

1, -1, -3, 1, 6, -1, -10, 1, 15, -1, -21, 1, 28, -1, -36, 1, 45, -1, -55, 1, 66, -1, -78, 1, 91, -1, -105, 1, 120, -1, -136, 1, 153, -1, -171, 1, 190, -1, -210, 1, 231, -1, -253, 1, 276, -1, -300, 1, 325, -1, -351, 1, 378, -1, -406, 1, 435, -1, -465, 1, 496, -1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Stefano Spezia, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,-3,0,-3,0,-1)

FORMULA

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

a(n) = C(n/2+2,2)*(-1)^(n/2)*(1+(-1)^n)/2 - (-1)^((n-1)/2)*(1-(-1)^n)/2.

E.g.f.: ((8-x^2)*cos(x) - (8 + 7*x)*sin(x))/8. - Stefano Spezia, Aug 08 2025

MATHEMATICA

CoefficientList[Series[(1-x-2x^3-x^5)/(1+x^2)^3, {x, 0, 61}], x] (* Stefano Spezia, Aug 08 2025 *)