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A099044 a(n) = (2*0^n + 3^n*binomial(2*n,n))/3. 3
1, 2, 18, 180, 1890, 20412, 224532, 2501928, 28146690, 318995820, 3636552348, 41655054168, 479033122932, 5527305264600, 63958818061800, 741922289516880, 8624846615633730, 100454095876204620, 1171964451889053900, 13693479385229998200 (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..900

FORMULA

G.f.: 1/3 + 4*x/(sqrt(1-12*x)(1-sqrt(1-12*x)))  = (1 + 2*sqrt(1-12*x))/(3*sqrt(1-12*x)).

n*a(n) +6*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 24 2012

MATHEMATICA

Join[{1}, Table[3^(n-1)*binomial(2*n, n), {n, 1, 30}]] (* G. C. Greubel, Dec 31 2017 *)

PROG

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

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

CROSSREFS

Cf. A069723, A088218, A099045, A099046.

Sequence in context: A132306 A264196 A214768 * A161122 A019581 A183285

Adjacent sequences:  A099041 A099042 A099043 * A099045 A099046 A099047

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 24 2004

STATUS

approved

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)