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

Author

N. J. A. Sloane, Jan 25 2001

Keywords

• nonn

Links

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

Crossrefs

Cf. A014847, A053214, A059289, A000108.

Programs

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 *)

PARI

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

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