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 A156739 #20 Sep 04 2024 18:57:59
%S A156739 1,1,1,1,120,1,1,3060,3060,1,1,38760,988380,38760,1,1,319770,
%T A156739 103285710,103285710,319770,1,1,1961256,5226256926,66199254396,
%U A156739 5226256926,1961256,1,1,9657700,157843517260,16494647553670,16494647553670,157843517260,9657700,1
%N A156739 Triangle T(n, k, m) = round( Product_{j=0..m} binomial(2*(n+j), 2*(k+j))/binomial( 2*(n-k+j), 2*j) ), where m = 6, read by rows.
%H A156739 G. C. Greubel, <a href="/A156739/b156739.txt">Rows n = 0..30 of the triangle, flattened</a>
%F A156739 T(n, k, m) = round( Product_{j=0..m} b(n+j, k+j)/b(n-k+j, j) ), where b(n, k) = binomial(2*n, 2*k) and m = 6.
%e A156739 Triangle begins as:
%e A156739 1;
%e A156739 1, 1;
%e A156739 1, 120, 1;
%e A156739 1, 3060, 3060, 1;
%e A156739 1, 38760, 988380, 38760, 1;
%e A156739 1, 319770, 103285710, 103285710, 319770, 1;
%e A156739 1, 1961256, 5226256926, 66199254396, 5226256926, 1961256, 1;
%t A156739 b[n_, k_]:= Binomial[2*n, 2*k];
%t A156739 T[n_, k_, m_]:= Round[Product[b[n+j, k+j]/b[n-k+j, j], {j,0,m}]];
%t A156739 Table[T[n, k, 6], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 18 2021 *)
%o A156739 (Magma)
%o A156739 A156739:= func< n,k | Round( (&*[Binomial(2*(n+j), 2*(k+j))/Binomial(2*(n-k+j), 2*j): j in [0..6]]) ) >;
%o A156739 [A156739(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 18 2021
%o A156739 (Sage)
%o A156739 def A156739(n, k): return round( product( binomial(2*(n+j), 2*(k+j))/binomial(2*(n-k+j), 2*j) for j in (0..6)) )
%o A156739 flatten([[A156739(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 18 2021
%Y A156739 Cf. A086645 (m=0), this sequence (m=6), A156740 (m=7), A156741 (m=8), A156742 (m=9).
%K A156739 nonn,tabl
%O A156739 0,5
%A A156739 _Roger L. Bagula_, Feb 14 2009
%E A156739 Definition corrected to give integral terms and edited by _G. C. Greubel_, Jun 18 2021