OFFSET
4,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 4..1000
FORMULA
G.f.: x^4*C(x)^9/(1 -x/sqrt(1-4*x)), where C(x) if the g.f. for Catalan numbers A000108. - G. C. Greubel, Jul 17 2019
a(n) ~ (3 - sqrt(5))^9 * (2 + sqrt(5))^(n+4) / (512*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019
D-finite with recurrence -(n+5)*(3013*n-9152)*a(n) +2*(15151*n^2+5919*n-112720)*a(n-1) +2*(-35029*n^2+9054*n-235442)*a(n-2) +6*(-19475*n^2+144598*n+188045)*a(n-3) +3*(131869*n^2-942353*n+1922276)*a(n-4) +2*(2*n-7)*(24721*n-92359)*a(n-5)=0. - R. J. Mathar, Nov 22 2024
MATHEMATICA
Drop[CoefficientList[Series[Sqrt[1-4x]*(1-Sqrt[1-4x])^9/(512*x^5*(Sqrt[1-4x]-x)), {x, 0, 40}], x], 4] (* G. C. Greubel, Jul 17 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(512*x^5*(sqrt(1-4*x) -x)) ) \\ G. C. Greubel, Jul 17 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^9/(512*x^5*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019
(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^9/(512*x^5*(sqrt(1-4*x)-x))).series(x, 40).coefficients(x, sparse=False); a[4:] # G. C. Greubel, Jul 17 2019
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
STATUS
approved