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 A289278 #19 Feb 16 2025 08:33:48
%S A289278 0,5,23,24,34,77,22,140,50,44,169,473,354,539,198,801,385,135,1207,
%T A289278 617,1483,52,2023,528,723,2273,2567,1265,1303,2813,550,233,1775,188,
%U A289278 2365,728,154,1520,4180,5585,571,236,3650,2672,714,4581,4966,2490,8931,4796,1566
%N A289278 a(n) = A005259(n) mod (2*n+1)^2.
%H A289278 Seiichi Manyama, <a href="/A289278/b289278.txt">Table of n, a(n) for n = 0..10000</a>
%H A289278 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AperyNumber.html">Apéry Number</a>
%F A289278 If m = 2*n + 1 is a prime, a(n) = A030211(n) mod m^2.
%t A289278 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 A289278 (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 A289278 Cf. A005259, A030211, A289277.
%K A289278 nonn
%O A289278 0,2
%A A289278 _Seiichi Manyama_, Jul 01 2017