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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A128015 Binomial coefficients C(2n+1,n) repeated. 1
1, 1, 3, 3, 10, 10, 35, 35, 126, 126, 462, 462, 1716, 1716, 6435, 6435, 24310, 24310, 92378, 92378, 352716, 352716, 1352078, 1352078, 5200300, 5200300, 20058300, 20058300, 77558760, 77558760, 300540195, 300540195 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A128017. Binomial transform is A005717(n+1).

LINKS

Table of n, a(n) for n=0..31.

FORMULA

G.f.: (1+x)*c(x^2)/sqrt(1-4x^2), c(x) the g.f. of A000108; E.g.f.: exp(-x)*dif(exp(x)*Bessel_I(1,2x),x); a(n)=C(n+1,n/2)(1+(-1)^n)/2+C(n,(n-1)/2)(1-(-1)^n)/2; as moment sequence a(n)=(1/(2*pi))int(x^n*x*(1+x)/sqrt(4-x^2),x,-2,2);

Conjecture: -(n+2)*(3*n-1)*a(n) -4*a(n-1) +4*n*(3*n+2)*a(n-2)=0. - R. J. Mathar, Jun 17 2016

MATHEMATICA

With[{c=Table[Binomial[2n+1, n], {n, 0, 20}]}, Riffle[c, c]] (* Harvey P. Dale, May 02 2012 *)

CROSSREFS

Sequence in context: A073709 A085288 A124630 * A233256 A218953 A081809

Adjacent sequences:  A128012 A128013 A128014 * A128016 A128017 A128018

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 11 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 17:16 EST 2016. Contains 278890 sequences.