A059288 a(n) = binomial(2*n,n) mod n.

0, 0, 2, 2, 2, 0, 2, 6, 2, 6, 2, 4, 2, 6, 0, 6, 2, 6, 2, 0, 6, 6, 2, 12, 2, 6, 20, 0, 2, 4, 2, 6, 9, 6, 7, 16, 2, 6, 20, 20, 2, 0, 2, 4, 0, 6, 2, 12, 2, 6, 3, 44, 2, 6, 32, 32, 39, 6, 2, 36, 2, 6, 12, 6, 5, 0, 2, 36, 66, 40, 2, 36, 2, 6, 45, 32, 0, 66, 2, 20, 20, 6, 2

Offset

1,3

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..5000 from T. D. Noe)

Formula

a(n) = Catalan(n) mod n. - Jonathan Sondow, Dec 13 2013

a(p) = 2, p an odd prime (provable using Wolstenholme's theorem). - David Trimas, Feb 11 2025

a(A014847(n)) = 0. - Amiram Eldar, Sep 26 2025

The case of a(p) = 2 for an odd prime p can also be proved using Wilson's theorem. - Julien Rouyer, Nov 14 2025

Maple

binomial(2*n, n) mod n;
seq(irem(binomial(2*n, n), n), n=1..83); # Zerinvary Lajos, Apr 20 2008

Mathematica

Table[Mod[Binomial[2*n, n], n], {n, 1, 25}] (* G. C. Greubel, Jan 04 2017 *)

Prog

(PARI) a(n) = binomial(2*n, n) % n; \\ Harry J. Smith, Jun 25 2009

Crossrefs

Cf. A014847, A053214, A059289, A000108.

Sequence in context: A215594 A230291 A338434 * A319109 A217670 A243310

Adjacent sequences: A059285 A059286 A059287 * A059289 A059290 A059291

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 25 2001

Status

approved