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 A116088 #13 Sep 08 2022 08:45:24
%S A116088 1,0,1,0,2,1,0,1,4,1,0,0,6,6,1,0,0,4,15,8,1,0,0,1,20,28,10,1,0,0,0,15,
%T A116088 56,45,12,1,0,0,0,6,70,120,66,14,1,0,0,0,1,56,210,220,91,16,1,0,0,0,0,
%U A116088 28,252,495,364,120,18,1
%N A116088 Riordan array (1, x*(1+x)^2).
%H A116088 Michael De Vlieger, <a href="/A116088/b116088.txt">Table of n, a(n) for n = 0..11475</a> (Rows 0 <= n <= 150).
%H A116088 Milan Janjić, <a href="https://www.emis.de/journals/JIS/VOL21/Janjic2/janjic103.html">Pascal Matrices and Restricted Words</a>, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
%F A116088 G.f.: 1/(1-x*y*(1+x)^2).
%F A116088 Number triangle T(n,k) = C(2*k, n-k) = C(n,k)*C(3*k,n)/C(3*k,k).
%e A116088 Triangle begins as:
%e A116088 1;
%e A116088 0, 1;
%e A116088 0, 2, 1;
%e A116088 0, 1, 4, 1;
%e A116088 0, 0, 6, 6, 1;
%e A116088 0, 0, 4, 15, 8, 1;
%e A116088 0, 0, 1, 20, 28, 10, 1;
%e A116088 0, 0, 0, 15, 56, 45, 12, 1;
%t A116088 Flatten[Table[Binomial[2k,n-k],{n,0,20},{k,0,n}]] (* _Harvey P. Dale_, Oct 22 2012 *)
%o A116088 (PARI) {T(n,k) = binomial(2*k, n-k)}; \\ _G. C. Greubel_, May 09 2019
%o A116088 (Magma) [[Binomial(2*k, n-k): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, May 09 2019
%o A116088 (Sage) [[binomial(2*k, n-k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, May 09 2019
%o A116088 (GAP) Flat(List([0..10], n->List([0..n], k-> Binomial(2*k, n-k) ))); # _G. C. Greubel_, May 09 2019
%Y A116088 Row sums are A002478. Diagonal sums are A094686. Inverse is (-1)^(n-k) * A109971(n,k). Unsigned version of A109970.
%K A116088 easy,nonn,tabl
%O A116088 0,5
%A A116088 _Paul Barry_, Feb 04 2006