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 A156367 #10 Jun 05 2021 06:36:16
%S A156367 1,1,1,1,3,2,1,6,10,6,1,10,30,42,24,1,15,70,168,216,120,1,21,140,504,
%T A156367 1080,1320,720,1,28,252,1260,3960,7920,9360,5040,1,36,420,2772,11880,
%U A156367 34320,65520,75600,40320,1,45,660,5544,30888,120120,327600,604800,685440,362880
%N A156367 Triangle T(n, k) = binomial(n+k, 2*k)*k!, read by rows.
%H A156367 Harvey P. Dale, <a href="/A156367/b156367.txt">Table of n, a(n) for n = 0..1000</a>
%F A156367 G.f.: 1/(1 -x -x*y/(1 -x -x*y/(1 -x -2*x*y/(1 -x -2*x*y/(1 -x -3*x*y/(1 -x -3*x*y/(1 - ... (continued fraction).
%F A156367 T(n, k) = binomial(n+k, 2*k)*k!
%F A156367 T(n, k) = A155856(n, n-k).
%F A156367 Sum_{k=0..n} T(n, k) = A155857(n).
%F A156367 sum_{k=0..floor(n/2)} T(n, k) = A084261(n).
%e A156367 Triangle begins
%e A156367 1;
%e A156367 1, 1;
%e A156367 1, 3, 2;
%e A156367 1, 6, 10, 6;
%e A156367 1, 10, 30, 42, 24;
%e A156367 1, 15, 70, 168, 216, 120;
%e A156367 1, 21, 140, 504, 1080, 1320, 720;
%e A156367 1, 28, 252, 1260, 3960, 7920, 9360, 5040;
%e A156367 1, 36, 420, 2772, 11880, 34320, 65520, 75600, 40320;
%t A156367 Flatten[Table[Binomial[n+k,2k]k!,{n,0,10},{k,0,n}]] (* _Harvey P. Dale_, Jun 17 2015 *)
%o A156367 (Sage) flatten([[factorial(k)*binomial(n+k, 2*k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 05 2021
%Y A156367 Cf. A084261 (diagonal sums), A155856 (row reversal), A155857 (row sums)
%K A156367 easy,nonn,tabl
%O A156367 0,5
%A A156367 _Paul Barry_, Feb 08 2009