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A026853
a(n) = T(2n,n+4), T given by A026736.
1
1, 10, 66, 365, 1837, 8741, 40133, 179932, 793605, 3460106, 14961664, 64306917, 275180827, 1173714565, 4994096327, 21211537533, 89972566673, 381261067469, 1614446775255, 6832832045575, 28908094009481, 122272843951891, 517095189163181
OFFSET
4,2
LINKS
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
Sequence in context: A080421 A320817 A004310 * A177452 A033504 A163615
KEYWORD
nonn,changed
STATUS
approved