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

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

Author

Asher Auel, Dec 16 1999

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A059288, A059289.

Programs

Haskell

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

Mathematica

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

PARI

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

Formula

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

Extensions

More terms from James Sellers, Dec 18 1999