A059289 -id:A059289 - cp's OEIS frontend

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

N. J. A. Sloane, Jan 25 2001

nonn

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

Cf. A014847, A053214, A059289, A000108.

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

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

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

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

A053214 Central binomial coefficients (A000984) read mod 2n, with a(0)=1.

Original entry on oeis.org

1, 0, 2, 2, 6, 2, 0, 2, 6, 2, 16, 2, 4, 2, 20, 0, 6, 2, 24, 2, 20, 6, 28, 2, 12, 2, 32, 20, 0, 2, 4, 2, 6, 42, 40, 42, 52, 2, 44, 20, 20, 2, 0, 2, 48, 0, 52, 2, 60, 2, 56, 54, 96, 2, 60, 32, 88, 96, 64, 2, 96, 2, 68, 12, 70, 70, 0, 2, 36, 66, 40, 2, 36, 2, 80, 120, 32, 0, 144, 2, 20, 20, 88

Offset: 0

Asher Auel, Dec 16 1999

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A059288, A059289.

a053214 0 = 1
a053214 n = a053200 (2 * n) n  -- Reinhard Zumkeller, Jan 24 2014

Join[{1}, Table[Mod[Binomial[2*n, n], 2*n], {n, 1, 100}]] (* G. C. Greubel, Sep 04 2018 *)

concat([1], vector(100, n, lift(Mod(binomial(2*n,n), 2*n)))) \\ G. C. Greubel, Sep 04 2018

a(n) = binomial(2*n, n) mod 2*n, with a(0)=1.

a(n) = A053200(2*n,n) for n > 0. - Reinhard Zumkeller, Jan 01 2013

More terms from James Sellers, Dec 18 1999

cp's OEIS Frontend

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

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