A127017 Expansion of 1/(1+6*x*c(x)), where c(x) = g.f. for Catalan numbers A000108.

1, -6, 30, -156, 798, -4116, 21132, -108792, 559134, -2876772, 14790660, -76080648, 391221516, -2012174664, 10347690072, -53218984176, 273689323038, -1407575396484, 7238848057812, -37228770844776, 191460735261828, -984660836306904, 5063949044206632, -26043244926688656

Offset: 0

Author

Philippe Deléham, Mar 21 2007

Keywords

• sign

Comments

Hankel transform is (-6)^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!( 1/(4 - 3*Sqrt(1-4*x)) )); // G. C. Greubel, May 31 2019

Maple

c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+6*x*c),x=0,27): seq(coeff(ser,x,n),n=0..23); # Emeric Deutsch, Mar 23 2007

Mathematica

CoefficientList[Series[1/(4-3*Sqrt[1-4*x]), {x,0,30}], x] (* G. C. Greubel, May 31 2019 *)

PARI

my(x='x+O('x^30)); Vec(1/(4-3*sqrt(1-4*x))) \\ G. C. Greubel, May 31 2019

Sage

(1/(4-3*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 31 2019

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-7)^k.

G.f.: 1/(4 - 3*sqrt(1-4*x)). - G. C. Greubel, May 31 2019

Extensions

More terms from Emeric Deutsch, Mar 23 2007