login
a(n) = A005259(n) mod 2*n+1.
2

%I #20 Jul 03 2017 04:28:10

%S 0,2,3,3,7,0,9,5,16,6,1,13,4,26,24,26,22,30,23,32,7,9,43,11,37,29,23,

%T 0,49,40,1,44,20,54,19,18,8,20,22,55,4,70,80,62,2,31,37,20,7,44,51,62,

%U 64,76,77,41,75,75,115,68,0,35,42,11,88,59,101,35,119,11

%N a(n) = A005259(n) mod 2*n+1.

%H Seiichi Manyama, <a href="/A289277/b289277.txt">Table of n, a(n) for n = 0..10000</a>

%H F. Beukers, <a href="http://dx.doi.org/10.1016/0022-314X(87)90025-4">Another congruence for the Apéry numbers</a>, J. Number Theory 25 (1987), no. 2, 201-210.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AperyNumber.html">Apéry Number</a>

%F If m = 2*n + 1 is a prime, a(n) = A030211(n) mod m.

%t Table[Mod[Sum[(Binomial[n, k] Binomial[n + k, k])^2, {k, 0, n}], 2n + 1], {n, 0, 100}] (* _Indranil Ghosh_, Jul 01 2017 *)

%o (PARI) a(n) = sum(k=0, n, (binomial(n, k)*binomial(n+k, k))^2) % (2*n+1); \\ _Michel Marcus_, Jul 01 2017

%Y Cf. A005259, A030211, A289278.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 01 2017