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 A179536 #10 Nov 09 2019 01:11:55
%S A179536 1,1,-1295,-11663,3732481,94348801,-12754875599,-662010720335,
%T A179536 43350090126337,4277886247480321,-117993200918257295,
%U A179536 -25968226221675142415,13219198014412583425,148460113964113254411265
%N A179536 a(n) = Sum_{k=0..n} binomial(n,k)^2*binomial(n-k,k)^2*(-324)^k.
%C A179536 On Jul 17 2010, _Zhi-Wei Sun_ introduced this sequence and made the following conjecture: If p is an odd prime with (p/13) = (-1/p) = 1 and p = x^2 + 13y^2 with x,y integers, then Sum_{k=0..p-1} a(k) == 4x^2 - 2p (mod p^2); if p is an odd prime with (p/13) = (-1/p) = -1 and 2p = x^2 + 13y^2 with x,y integers, then Sum_{k=0..p-1} a(k) == 2x^2 - 2p (mod p^2); if p > 3 is a prime with (p/13) = -(-1/p), then Sum_{k=0..p-1} a(k) == 0 (mod p^2). He also conjectured that Sum_{k=0..n-1} (260k+237)*a(k) == 0 (mod n) for all n=1,2,3,... and that Sum_{k=0..p-1} (260k+237)*a(k) == p(130(-1/p)+107) (mod p^2) for any prime p > 3.
%H A179536 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 A179536 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 A179536 For n=2 we have a(2) = 1 + 2^2*(-324) = -1295.
%t A179536 a[n_]:=Sum[Binomial[n,k]^2Binomial[n-k,k]^2*(-324)^k,{k,0,n}] Table[a[n],{n,0,25}]
%K A179536 sign
%O A179536 0,3
%A A179536 _Zhi-Wei Sun_, Jul 18 2010