This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A289277 #21 Feb 16 2025 08:33:48
%S A289277 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 A289277 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 A289277 64,76,77,41,75,75,115,68,0,35,42,11,88,59,101,35,119,11
%N A289277 a(n) = A005259(n) mod 2*n+1.
%H A289277 Seiichi Manyama, <a href="/A289277/b289277.txt">Table of n, a(n) for n = 0..10000</a>
%H A289277 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 A289277 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AperyNumber.html">Apéry Number</a>
%F A289277 If m = 2*n + 1 is a prime, a(n) = A030211(n) mod m.
%t A289277 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 A289277 (PARI) a(n) = sum(k=0, n, (binomial(n, k)*binomial(n+k, k))^2) % (2*n+1); \\ _Michel Marcus_, Jul 01 2017
%Y A289277 Cf. A005259, A030211, A289278.
%K A289277 nonn
%O A289277 0,2
%A A289277 _Seiichi Manyama_, Jul 01 2017