A098399 a(n) = 3^n*binomial(2*n+1, n).

1, 9, 90, 945, 10206, 112266, 1250964, 14073345, 159497910, 1818276174, 20827527084, 239516561466, 2763652632300, 31979409030900, 370961144758440, 4312423307816865, 50227047938102310, 585982225944526950, 6846739692614999100, 80106854403595489470, 938394580156404305220

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

G.f.: (1-sqrt(1-12*x))/(6*x*sqrt(1-12*x)).

E.g.f.: a(n) = n!* [x^n] exp(6*x)*(BesselI(0, 6*x) + BesselI(1, 6*x)). - Peter Luschny, Aug 25 2012

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

From G. C. Greubel, Dec 27 2023: (Start)

a(n) = 3^n * (2*n+1)*A000108(n).

a(n) = (2*n+1)*A005159(n).

a(n) = 3^n * A001700(n). (End)

From Amiram Eldar, Jan 16 2024: (Start)

Sum_{n>=0} 1/a(n) = 6/11 + 72*arcsin(1/(2*sqrt(3)))/(11*sqrt(11)).

Sum_{n>=0} (-1)^n/a(n) = 6/13 + 72*arcsinh(1/(2*sqrt(3)))/(13*sqrt(13)). (End)

Maple

Z:=(1-sqrt(1-3*z))*4^n/sqrt(1-3*z)/6: Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=1..18); # Zerinvary Lajos, Jan 01 2007

Mathematica

Table[3^n Binomial[2n+1, n], {n, 0, 20}] (* Harvey P. Dale, Mar 28 2012 *)

Prog

(Magma) [3^n*Binomial(2*n+1, n): n in [ 0..20]]; // Vincenzo Librandi, Noc 24 2012
(PARI) a(n)=binomial(2*n+1, n)*3^n \\ Charles R Greathouse IV, Oct 23 2023
(SageMath) [3^n*binomial(2*n+1, n) for n in range(21)] # G. C. Greubel, Dec 27 2023

Crossrefs

Cf. A000108, A001700, A005159, A069720, A069723, A098400.

Sequence in context: A155199 A147841 A036258 * A264914 A143079 A233829

Adjacent sequences: A098396 A098397 A098398 * A098400 A098401 A098402

Keyword

easy,nonn

Author

Paul Barry, Sep 06 2004

Status

approved