A127053 Expansion of 1/(1+9*x*c(x)), where c(x) = g.f. for Catalan numbers A000108.

1, -9, 72, -585, 4734, -38358, 310662, -2516481, 20383110, -165104478, 1337341896, -10832484474, 87743071332, -710719065000, 5756823757890, -46630274845905, 377705217526470, -3059412293786310, 24781239462988800, -200728040080084110, 1625897123058144420

Offset: 0

Author

Philippe Deléham, Mar 21 2007

Keywords

• sign

Comments

Hankel transform is (-9)^n.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A039599.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(11-9*Sqrt(1-4*x)) )); // G. C. Greubel, May 28 2019

Maple

c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+9*x*c),x=0,24): seq(coeff(ser,x,n),n=0..21); # Emeric Deutsch, Mar 23 2007

Mathematica

CoefficientList[Series[2/(11-9*Sqrt[1-4*x]), {x, 0, 30}], x] (* G. C. Greubel, May 28 2019 *)

PARI

my(x='x+O('x^30)); Vec(2/(11-9*sqrt(1-4*x))) \\ G. C. Greubel, May 28 2019

Sage

(2/(11-9*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-10)^k.

G.f.: 2/(11 - 9*sqrt(1-4*x)). - G. C. Greubel, May 28 2019

Extensions

More terms from Emeric Deutsch, Mar 23 2007