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!)
A099045 a(n) = (3*0^n + 4^n*binomial(2*n,n))/4. 4
1, 2, 24, 320, 4480, 64512, 946176, 14057472, 210862080, 3186360320, 48432676864, 739699064832, 11342052327424, 174493112729600, 2692179453542400, 41639042214789120, 645405154329231360, 10022762396642181120, 155909637281100595200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

(1 + (k-1)*sqrt(1-4*k*x))/(k*sqrt(1-4*k*x)) is the g.f. for ((k-1)*0^n + k^n*binomial(2*n,n))/k.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..800

FORMULA

G.f.: (1+3*sqrt(1-16*x))/(4*sqrt(1-16*x)).

n*a(n) +8*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 24 2012

E.g.f.: (3 + exp(8*x) * BesselI(0,8*x)) / 4. - Ilya Gutkovskiy, Nov 17 2021

MATHEMATICA

Join[{1}, Table[4^(n-1)*Binomial[2*n, n], {n, 1, 30}]] (* G. C. Greubel, Dec 31 2017 *)

PROG

(MAGMA) [(3*0^n + 4^n*Binomial(2*n, n))/4: n in [ 0..20]]; // Vincenzo Librandi, Nov 24 2012

(PARI) for(n=0, 30, print1((3*0^n + 4^n*binomial(2*n, n))/4, ", ")) \\ G. C. Greubel, Dec 31 2017

CROSSREFS

Cf. A069723, A088218, A099044, A099046.

Sequence in context: A246610 A119491 A001864 * A181174 A209290 A333715

Adjacent sequences:  A099042 A099043 A099044 * A099046 A099047 A099048

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 24 2004

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 17 06:27 EDT 2022. Contains 353730 sequences. (Running on oeis4.)