A144485 a(n) = (3n + 2)*binomial(3n + 1,n).

2, 20, 168, 1320, 10010, 74256, 542640, 3922512, 28120950, 200300100, 1419269280, 10013421600, 70394353848, 493362138080, 3448674255840, 24051721745568, 167405449649550, 1163116182943260, 8068463611408200, 55891260077406600

Offset: 0

Author

Roger L. Bagula, Oct 12 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Ömer Eğecioğlu, Timothy Redmond, and Charles Ryavec, Almost product evaluation of Hankel Determinants, The Electronic Journal of Combinatorics, Vol. 15, No. 1 (2008), #R6; arXiv preprint, arXiv:0704.3398 [math.CO], 2007.

Crossrefs

Cf. A005809, A045721, A090763, A210453.

Programs

Magma

[(3*n+2)*Binomial(3*n+1, n): n in [0..20]]; // Vincenzo Librandi, Feb 14 2014

Maple

a:= proc(n) option remember; `if`(n=0, 2,
      3*(3*n+1)*(3*n+2)*a(n-1)/(2*n*(2*n+1)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 01 2014

Mathematica

a[k_] = (3k + 2)Binomial[3k + 1, k]; Table[a[k], {k, 0, 30}]

Formula

a(n) = (3n+2)*A045721(n). - R. J. Mathar, Feb 01 2014

a(n) = 2*A090763(n). - Alois P. Heinz, Feb 01 2014

From Amiram Eldar, Dec 07 2024: (Start)

a(n) = 2 * (n+1) * A005809(n+1) / 3.

Sum_{n>=0} 1/a(n) = (3/2) * A210453. (End)