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 A179537 #5 Jan 12 2019 08:06:47
%S A179537 1,1,-63,-575,6913,224001,420801,-69020223,-918270975,14596918273,
%T A179537 511845045697,336721812417,-198449271643391,-2498857696947455,
%U A179537 51614254703660481,1666776235855331265,-1588877076116525055
%N A179537 a(n) = Sum_{k=0..n} binomial(n,k)^2*binomial(n-k,k)^2*(-16)^k.
%C A179537 On July 17, 2010 Zhi-Wei Sun introduced this sequence and made the following conjecture: If p is a prime with (p/7)=1 and p=x^2+7y^2 with x,y integers, then sum_{k=0}^{p-1}(-1)^k*a(k)=4x^2-2p (mod p^2); if p is a prime with (p/7)=-1, then sum_{k=0}^{p-1}(-1)^k*a(k)=0 (mod p^2). He also conjectured that sum_{k=0}^{n-1}(42k+37)(-1)^k*a(k)=0 (mod n) for all n=1,2,3,... and that sum_{k=0}^{p-1}(42k+37)(-1)^k*a(k)=p(21(p/7)+16) (mod p^2) for any prime p.
%H A179537 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 A179537 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.
%e A179537 For n=2 we have a(2)=1+2^2*(-16)=-63.
%t A179537 a[n_]:=Sum[Binomial[n,k]^2Binomial[n-k,k]^2*(-16)^k,{k,0,n}] Table[a[n],{n,0,25}]
%Y A179537 Cf. A179536, A179535, A179524, A178790, A178791, A178808, A173774.
%K A179537 sign
%O A179537 0,3
%A A179537 _Zhi-Wei Sun_, Jul 18 2010