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a(n) = A005259(n) mod (n+1)^3.
1

%I #14 Jul 02 2017 06:13:51

%S 0,5,19,37,1,149,1,165,559,5,1,1373,1,5,2698,2725,1,581,1,2445,3160,5,

%T 1,8285,1751,5,15139,9677,1,18005,1,31397,16045,5,13450,2669,1,5,

%U 52801,20365,1,20501,1,65333,59425,5,1,86621,48707,99005,59029,54173,1,99725

%N a(n) = A005259(n) mod (n+1)^3.

%H Seiichi Manyama, <a href="/A289289/b289289.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 = n + 1 is a prime and m >= 5, a(n) = 1.

%o (PARI) a(n) = sum(k=0, n, (binomial(n, k)*binomial(n+k, k))^2) % (n+1)^3; \\ _Michel Marcus_, Jul 02 2017

%Y Cf. A005259, A276323.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 01 2017