A127769 a(n) = 3*C(4*n-2,2*n)/(2*n+1) - 2*0^n.

1, 1, 9, 90, 1001, 11934, 149226, 1931540, 25662825, 347993910, 4796857230, 67016296620, 946844533674, 13505406670700, 194214400834356, 2812744285440936, 40989428837821289, 600607911737487654, 8843512890953152230, 130783058462384959036, 1941701670546516308430

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = A127768(2*n).

Conjecture: n*(2*n+1)*(2*n-3)*a(n) - 2*(4*n-5)*(4*n-3)*(2*n-1)*a(n-1) = 0, n > 1. - R. J. Mathar, Nov 12 2014

a(n) ~ 3 * 2^(4*n-7/2) / (n^(3/2) * sqrt(Pi)). - Amiram Eldar, Jan 25 2026

Mathematica

Join[{1}, Table[(3*Binomial[4n-2, 2n])/(2n+1), {n, 20}]] (* Harvey P. Dale, Mar 14 2012 *)

Crossrefs

Cf. A127768.

Sequence in context: A082367 A276506 A049389 * A276961 A062815 A294610

Adjacent sequences: A127766 A127767 A127768 * A127770 A127771 A127772

Keyword

easy,nonn

Author

Paul Barry, Jan 28 2007

Status

approved