A126982 Expansion of 1/(1+3*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

1, -3, 6, -15, 30, -78, 144, -423, 630, -2490, 1956, -16998, -5844, -142860, -235740, -1475415, -3951450, -17627490, -57571740, -228692610, -810889020, -3098590020, -11377872720, -43011709110, -160518364740, -606261789828

Offset: 0

Author

Philippe Deléham, Mar 21 2007

Keywords

• sign

Comments

Hankel transform is (-3)^n.

Catalan transform of the sequence (-1)^n*A000244(n). - R. J. Mathar, Nov 11 2008

Links

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

Crossrefs

Cf. A000108, A000244, A039599.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(5-3*Sqrt(1-4*x)) )); // G. C. Greubel, May 28 2019

Mathematica

CoefficientList[Series[2/(5-3*Sqrt[1-4*x]), {x,0,30}], x] (* G. C. Greubel, May 28 2019 *)

PARI

my(x='x+O('x^30)); Vec(2/(5-3*sqrt(1-4*x))) \\ G. C. Greubel, May 28 2019

Sage

(2/(5-3*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)*(-4)^k.

G.f.: 2/(5 - 3*sqrt(1-4*x)). - G. C. Greubel, May 28 2019

D-finite with recurrence 4*n*a(n) +(-7*n+24)*a(n-1) +18*(-2*n+3)*a(n-2)=0. - R. J. Mathar, Nov 22 2024

Extensions

Extended by R. J. Mathar, Nov 11 2008