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 A227964 #8 Dec 17 2013 12:42:01
%S A227964 1,1,-1,-1,1,1,-2,-1,4,-1,-2,1,1,-3,0,8,-6,-6,8,0,-3,1,1,-4,2,12,-17,
%T A227964 -8,28,-8,-17,12,2,-4,1,1,-5,5,15,-35,-1,65,-45,-45,65,-1,-35,15,5,-5,
%U A227964 1,1,-6,9,16,-60,24,116,-144,-66,220,-66,-144,116,24,-60,16,9,-6,1,1,-7,14,14,-91,77,168,-344,-14,546,-364,-364,546,-14,-344,168,77,-91,14,14,-7,1
%N A227964 Triangle where the g.f. of row n equals (1-x-x^2+x^3)^n and terms T(n,k) are read by rows n>=0, k=0..3*n.
%H A227964 Paul D. Hanna, <a href="/A227964/b227964.txt">Table of n, a(n) for n = 0..2500</a>
%F A227964 Sum_{k=0..3*n} |T(n,k)| = A192205(n).
%F A227964 Sum_{k=0..3*n} T(n,k)^2 = binomial(4*n,n).
%F A227964 Sum_{k=0..3*n} T(n,k) * binomial(3*n,k) = (-1)^n * binomial(4*n,n).
%F A227964 Sum_{k=0..3*n} T(n,k) * binomial(2*n+k,k) = 2^n.
%F A227964 Sum_{k=0..3*n} T(n,k) * binomial(3*n+k,k) = A008288(3*n,n), where A008288 is the Delannoy array (see A026001).
%e A227964 Triangle begins:
%e A227964 1;
%e A227964 1, -1, -1, 1;
%e A227964 1, -2, -1, 4, -1, -2, 1;
%e A227964 1, -3, 0, 8, -6, -6, 8, 0, -3, 1;
%e A227964 1, -4, 2, 12, -17, -8, 28, -8, -17, 12, 2, -4, 1;
%e A227964 1, -5, 5, 15, -35, -1, 65, -45, -45, 65, -1, -35, 15, 5, -5, 1;
%e A227964 1, -6, 9, 16, -60, 24, 116, -144, -66, 220, -66, -144, 116, 24, -60, 16, 9, -6, 1;
%e A227964 1, -7, 14, 14, -91, 77, 168, -344, -14, 546, -364, -364, 546, -14, -344, 168, 77, -91, 14, 14, -7, 1; ...
%o A227964 (PARI) {T(n,k)=polcoeff((1-x-x^2+x^3 +x*O(x^k))^n,k)}
%o A227964 for(n=0,10,for(k=0,3*n,print1(T(n,k),", "));print(""))
%Y A227964 Cf. A192205.
%K A227964 sign,tabf
%O A227964 0,7
%A A227964 _Paul D. Hanna_, Aug 01 2013