The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126986 Expansion of 1/(1+4*x*c(x)), c(x) the g.f. of Catalan numbers A000108. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Hankel transform is (-4)^n.
For n>=37, all terms are negative. - Vaclav Kotesovec, May 30 2019
LINKS
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
KEYWORD
sign
AUTHOR
Philippe Deléham, Mar 21 2007
EXTENSIONS
More terms from Emeric Deutsch, Mar 23 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 15:58 EDT 2024. Contains 372800 sequences. (Running on oeis4.)