A126984 Expansion of 1/(1+2*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

1, -2, 2, -4, 2, -12, -12, -72, -190, -700, -2308, -8120, -28364, -100856, -360792, -1301904, -4727358, -17268636, -63405012, -233885784, -866327748, -3220976616, -12016209192, -44966763504, -168750724428, -634935132312, -2394717424552, -9051945482032

Offset

0,2

Comments

Hankel transform is (-2)^n.

Hankel transform omitting first term is (-2)^n omitting first term. Hankel transform omitting first two terms is 2*(-1)^n*A014480(n). - Michael Somos, May 16 2022

Links

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

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-3)^k.

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

(-1)^n*a(n) = A268600(n) - A268601(n). - Michael Somos, May 16 2022

Maple

c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+2*x*c), x=0, 32): seq(coeff(ser, x, n), n=0..30); # Emeric Deutsch, Mar 24 2007

Mathematica

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

Prog

(PARI) my(x='x+O('x^30)); Vec(1/(2-sqrt(1-4*x))) \\ G. C. Greubel, May 28 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(2-Sqrt(1-4*x)) )); // G. C. Greubel, May 28 2019
(Sage) (1/(2-sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019

Crossrefs

Cf. A000108, A014480, A039599, A268600, A268601.

Sequence in context: A010026 A059427 A137777 * A159749 A227293 A331391

Adjacent sequences: A126981 A126982 A126983 * A126985 A126986 A126987

Keyword

sign

Author

Philippe Deléham, Mar 21 2007

Extensions

Corrected and extended by Emeric Deutsch, Mar 24 2007

Status

approved