A053214 - OEIS

%I #17 Oct 27 2023 22:00:45

%S 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,

%T 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,

%U 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

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

%H G. C. Greubel, <a href="/A053214/b053214.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = A053200(2*n,n) for n > 0. - _Reinhard Zumkeller_, Jan 01 2013

%t Join[{1}, Table[Mod[Binomial[2*n, n], 2*n], {n, 1, 100}]] (* _G. C. Greubel_, Sep 04 2018 *)

%o (Haskell)

%o a053214 0 = 1

%o a053214 n = a053200 (2 * n) n  -- _Reinhard Zumkeller_, Jan 24 2014

%o (PARI) concat([1], vector(100, n, lift(Mod(binomial(2*n,n), 2*n)))) \\ _G. C. Greubel_, Sep 04 2018

%Y Cf. A059288, A059289.

%K nonn,easy

%O 0,3

%A _Asher Auel_, Dec 16 1999

%E More terms from _James A. Sellers_, Dec 18 1999