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 A179524 #7 Jan 12 2019 08:06:24
%S A179524 1,1,-15,-143,1,12801,100401,-555855,-16006143,-69903359,1371541105,
%T A179524 20881151985,5878439425,-2725373454335,-25310084063055,
%U A179524 145439041081137,4851621446905857,23952290336559105,-470461357757965071,-7793050905481342863,-4149447893184517119
%N A179524 a(n) = Sum_{k=0..n} (-4)^k*binomial(n,k)^2*binomial(n-k,k)^2.
%C A179524 On July 1, 2010 Zhi-Wei Sun introduced this sequence and made the following conjecture: If p is a prime with p=1,9 (mod 20) and p=x^2+5y^2 with x,y integers, then sum_{k=0}^{p-1}a(k)=4x^2-2p (mod p^2); if p is a prime with p=3,7 (mod 20) and 2p=x^2+5y^2 with x,y integers, then sum_{k=0}^{p-1}a(k)=2x^2-2p (mod p^2); if p is a prime with p=11,13,17,19 (mod 20), then sum_{k=0}^{p-1}w_k=0 (mod p^2). He also conjectured that sum_{k=0}^{n-1}(20k+17)w_k=0 (mod n) for all n=1,2,3,... and that sum_{k=0}^{p-1}(20k+17)w_k=p(10(-1/p)+7) (mod p^2) for any odd prime p. Sun also formulated similar conjectures for some sequences similar to a(n).
%H A179524 Zhi-Wei Sun, <a href="http://arxiv.org/abs/0911.5665">Open Conjectures on Congruences</a>, preprint, arXiv:0911.5665 [math.NT], 2009-2011.
%H A179524 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1006.2776">On Apery numbers and generalized central trinomial coefficients</a>, preprint, arXiv:1006.2776 [math.NT], 2010-2011.
%F A179524 a(n) = Sum_{k=0..[n/2]} (-4)^k*binomial(n,2k)^2*binomial(2k,k)^2.
%e A179524 For n=3 we have a(3)=1-4*3^2*2^2=-143.
%t A179524 W[n_]:=Sum[(-4)^k*Binomial[n,k]^2*Binomial[n-k,k]^2,{k,0,n}] Table[W[n],{n,0,50}]
%Y A179524 Cf. A005259, A178790, A178791, A178808, A179508, A173774.
%K A179524 sign
%O A179524 0,3
%A A179524 _Zhi-Wei Sun_, Jul 17 2010