A126986 Expansion of 1/(1+4*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

1, -4, 12, -40, 124, -408, 1272, -4176, 13020, -42808, 133096, -439344, 1358872, -4514800, 13853040, -46469280, 140945820, -479312760, 1430085000, -4958382960, 14453014920, -51500944080, 145230007440, -537922074720, 1446902948184, -5662012752048, 14228883685392

Offset

0,2

Comments

Hankel transform is (-4)^n.

For n>=37, all terms are negative. - Vaclav Kotesovec, May 30 2019

Links

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

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-5)^k.

G.f.: 1/(3 - 2*sqrt(1-4*x)). - G. C. Greubel, May 29 2019

a(n) ~ -4^n / (9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, May 30 2019

Maple

c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+4*x*c), x=0, 30): seq(coeff(ser, x, n), n=0..27); # Emeric Deutsch, Mar 23 2007

Mathematica

CoefficientList[Series[1/(3-2*Sqrt[1-4*x]), {x, 0, 30}], x] (* G. C. Greubel, May 29 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(1/(3-2*sqrt(1-4*x))) \\ G. C. Greubel, May 29 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/(3 - 2*Sqrt(1-4*x)) )); // G. C. Greubel, May 29 2019
(Sage) (1/(3-2*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 29 2019

Crossrefs

Sequence in context: A335806 A058353 A104525 * A341990 A090576 A152174

Adjacent sequences: A126983 A126984 A126985 * A126987 A126988 A126989

Keyword

sign

Author

Philippe Deléham, Mar 21 2007

Extensions

More terms from Emeric Deutsch, Mar 23 2007

Status

approved