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 A338035 #13 Oct 14 2020 11:10:13
%S A338035 1,2,1,1,5,1,0,12,8,1,0,19,33,11,1,0,21,96,63,14,1,0,15,217,256,102,
%T A338035 17,1,0,6,386,830,524,150,20,1,0,1,533,2241,2147,927,207,23,1,0,0,560,
%U A338035 5079,7440,4541,1492,273,26,1
%N A338035 Triangle T(n,m) = (1/m)*Sum_{k=1..m} k*C(2*m-k-1,m-k)*C(2*(2*m-k),n-2*m+k), n>0, m>0.
%F A338035 G.f.: 1/(1-(1-sqrt(x*(-4*x^5-16*x^4-24*x^3-16*x^2-4*x)*y+1))/(2*x^3+4*x^2+2*x)).
%e A338035 1,
%e A338035 2,1,
%e A338035 1,5,1,
%e A338035 0,12,8,1,
%e A338035 0,19,33,11,1,
%e A338035 0,21,96,63,14,1,
%e A338035 0,15,217,256,102,17,1
%t A338035 T[n_, m_] := Sum[k * Binomial[2*m - k - 1, m - k] * Binomial[2*(2*m - k), n - 2*m + k], {k, 1, m}] / m; Table[T[n, m], {n, 1, 10}, {m, 1, n}] // Flatten (* _Amiram Eldar_, Oct 08 2020 *)
%o A338035 (Maxima)
%o A338035 T(n,m):=sum(k*binomial(2*m-k-1,m-k)*binomial(2*(2*m-k),n-2*m+k),k,1,m)/m;
%Y A338035 Cf. A338036, A338037.
%K A338035 nonn,tabl
%O A338035 1,2
%A A338035 _Vladimir Kruchinin_, Oct 07 2020