login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158499 Expansion of (1+sqrt(1-4x))/(2-4x). 1
1, 1, 1, 0, -5, -24, -90, -312, -1053, -3536, -11934, -40664, -140114, -488240, -1719380, -6113200, -21921245, -79200160, -288045110, -1053728920, -3874721030, -14313562480, -53093391980, -197669347600, -738398308850, -2766700765024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Hankel transform is A056594 with g.f. 1/(1+x^2).

Row sums of the Riordan array (sqrt(1-4x)/(1-2x),xc(x)^2), c(x) the g.f. of A000108.

The inverse Catalan transform yields A146559. - R. J. Mathar, Mar 20 2009

LINKS

Matthew House, Table of n, a(n) for n = 0..1669

FORMULA

a(n) = Sum_{k=0..n} binomial(2k,k)*A158495(n-k).

Conjecture: n*a(n) +6*(1-n)*a(n-1) +4*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 14 2011

This conjecture has been proven. - Matthew House, Nov 08 2015

MATHEMATICA

CoefficientList[ Series[(1 + Sqrt[1 - 4x])/(2 - 4x), {x, 0, 26}], x] (* Robert G. Wilson v, Nov 08 2015 *)

PROG

(PARI) x='x+O('x^33); Vec(((1-4*x)+sqrt(1-4*x))/(2*(1-2*x)*sqrt(1-4*x))) \\ Altug Alkan, Nov 08 2015

CROSSREFS

Sequence in context: A089095 A220316 A220339 * A074085 A145914 A066316

Adjacent sequences:  A158496 A158497 A158498 * A158500 A158501 A158502

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 20 2009

EXTENSIONS

Name edited by Matthew House, Nov 08 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)