A126987 Expansion of 1/(1+5*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

1, -5, 20, -85, 350, -1470, 6090, -25485, 105830, -442150, 1838240, -7673330, 31923220, -133186760, 554325750, -2311919325, 9624918150, -40133290350, 167114005800, -696706389750, 2901470571300, -12094930814100, 50375156502900, -209972720898450, 874600454065500

Offset

0,2

Comments

Hankel transform is (-5)^n.

Links

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

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-6)^k.

G.f.: 2/(7 - 5*sqrt(1-4*x)). - G. C. Greubel, May 29 2019

Maple

c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+5*x*c), x=0, 27): seq(coeff(ser, x, n), n=0..24); # Emeric Deutsch, Mar 23 2007

Mathematica

CoefficientList[Series[2/(7-5*Sqrt[1-4*x]), {x, 0, 30}], x] (* G. C. Greubel, May 29 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(2/(7-5*sqrt(1-4*x))) \\ G. C. Greubel, May 29 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(7 - 5*Sqrt(1-4*x)) )); // G. C. Greubel, May 29 2019
(Sage) (2/(7-5*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 29 2019

Crossrefs

Cf. A000108, A039599.

Sequence in context: A006231 A373340 A069007 * A152185 A152187 A341920

Adjacent sequences: A126984 A126985 A126986 * A126988 A126989 A126990

Keyword

sign

Author

Philippe Deléham, Mar 21 2007

Extensions

More terms from Emeric Deutsch, Mar 23 2007

Status

approved