OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = c(n)*h(n) where c(n) = Catalan(n)*((n-3)*(n+1))/((2*n-3)*(2*n-1)) and h(n) = hypergeom([1, -n], [5/2 - n], 3/4).
D-finite with recurrence: n*a(n) +(-13*n+15)*a(n-1) +4*(16*n-37)*a(n-2) +2*(-71*n+245)*a(n-3) +60*(2*n-9)*a(n-4)=0. - R. J. Mathar, Jan 23 2020
MAPLE
MATHEMATICA
CoefficientList[Series[-(10x^2 - 6x + 1) Sqrt[1 - 4x]/(3x - 1)^2, {x, 0, 28}], x]
PROG
(PARI) x='x+O('x^40); Vec(-(10*x^2-6*x+1)*sqrt(1-4*x)/(1-3*x)^2) \\ G. C. Greubel, Oct 27 2018
(Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(-(10*x^2-6*x+1)*Sqrt(1-4*x)/(1-3*x)^2)); // G. C. Greubel, Oct 27 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Oct 22 2018
STATUS
approved