A166337 a(n) = (2n+0^n)*C(4n,2n).

1, 12, 280, 5544, 102960, 1847560, 32449872, 561632400, 9617286240, 163352435400, 2756930576400, 46290177201840, 773942488394400, 12893881856650704, 214163336821292320, 3547937446945842720, 58643972510162897088, 967403410158179609160, 15930451449966124051344

Offset

0,2

Comments

The aerated sequence gives the central coefficients in number triangle A166335.

Links

Table of n, a(n) for n=0..18.

Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, and Helmut Prodinger, Some Binomial Sums Involving Absolute Values, Journal of Integer Sequences, Vol. 19 (2016), Article 16.3.7; arXiv preprint, arXiv:1411.1477v2 [math.CO], 2014-2016. See eq. (24).

Formula

D-finite with recurrence (2*n-1)*(n-1)*a(n) - 2*(4*n-1)*(4*n-3)*a(n-1) = 0. - R. J. Mathar, Feb 27 2023

a(n) ~ 2^(4*n+1/2) * sqrt(n/Pi). - Amiram Eldar, Oct 23 2025

Mathematica

Join[{1}, Table[(2n)*Binomial[4n, 2n], {n, 20}]] (* Harvey P. Dale, Jan 21 2015 *)

Crossrefs

Cf. A001448.

Sequence in context: A351765 A295037 A295528 * A183767 A009604 A154669

Adjacent sequences: A166334 A166335 A166336 * A166338 A166339 A166340

Keyword

easy,nonn

Author

Paul Barry, Oct 12 2009

Status

approved