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A257589
a(n) = (2n+1)^2*Catalan(n).
1
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
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: A222993 A171480 A369906 * A341921 A231413 A007681
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 10 2015
STATUS
approved