A257589 a(n) = (2n+1)^2*Catalan(n).

1, 9, 50, 245, 1134, 5082, 22308, 96525, 413270, 1755182, 7407036, 31097794, 130007500, 541574100, 2249204040, 9316746045, 38504502630, 158814867750, 653887380300, 2688007311990, 11034286426020, 45238127719980, 185252191371000, 757818686552850, 3097059857724924

Offset

0,2

Links

Table of n, a(n) for n=0..24.

G.-S. Cheon, H. Kim, and L. W. Shapiro, Mutation effects in ordered trees, arXiv preprint arXiv:1410.1249 [math.CO], 2014 (see page 10).

Formula

a(n) = A016754(n)*A000108(n). - Michel Marcus, Jun 11 2019

a(n) = (n + 1/2)*(2*n + 2)! / (n + 1)!^2. - Peter Luschny, Feb 15 2023

Sum_{n>=0} 1/a(n) = Pi/(3*sqrt(3)) - log(2+sqrt(3))*Pi/6 + 4*G/3, where G is Catalan's constant (A006752). - Amiram Eldar, Feb 16 2023

Maple

a := n -> (n + 1/2)*(2*n + 2)!/(n + 1)!^2: seq(a(n), n = 0..22); # Peter Luschny, Feb 15 2023

Mathematica

Table[(2n+1)^2 CatalanNumber[n], {n, 0, 30}] (* Harvey P. Dale, Sep 02 2015 *)

Prog

(PARI) a(n) = (2*n+1)^2*binomial(2*n, n)/(n+1); \\ Michel Marcus, Jun 11 2019

Crossrefs

Cf. A000108 (Catalan), A016754 (odd squares), A006752.

Sequence in context: A279979 A222993 A171480 * A341921 A231413 A007681

Adjacent sequences: A257586 A257587 A257588 * A257590 A257591 A257592

Keyword

nonn

Author

N. J. A. Sloane, May 10 2015

Status

approved