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%I #18 Jul 03 2017 04:28:18
%S 0,5,23,24,34,77,22,140,50,44,169,473,354,539,198,801,385,135,1207,
%T 617,1483,52,2023,528,723,2273,2567,1265,1303,2813,550,233,1775,188,
%U 2365,728,154,1520,4180,5585,571,236,3650,2672,714,4581,4966,2490,8931,4796,1566
%N a(n) = A005259(n) mod (2*n+1)^2.
%H Seiichi Manyama, <a href="/A289278/b289278.txt">Table of n, a(n) for n = 0..10000</a>
%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^2.
%t Table[Mod[Sum[(Binomial[n, k] Binomial[n + k, k])^2, {k, 0, n}], (2n + 1)^2], {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)^2; \\ _Michel Marcus_, Jul 01 2017
%Y Cf. A005259, A030211, A289277.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 01 2017