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 A156741 #13 Sep 04 2024 18:58:16
%S A156741 1,1,1,1,190,1,1,7315,7315,1,1,134596,5181946,134596,1,1,1562275,
%T A156741 1106715610,1106715610,1562275,1,1,13123110,107904771975,
%U A156741 1985447804340,107904771975,13123110,1,1,86493225,5974000557525,1275875833357125,1275875833357125,5974000557525,86493225,1
%N A156741 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 = 8, read by rows.
%H A156741 G. C. Greubel, <a href="/A156741/b156741.txt">Rows n = 0..30 of the triangle, flattened</a>
%F A156741 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 = 8.
%F A156741 Sum_{k=0..n} T(n, k) = A151709(n).
%e A156741 Triangle begins as:
%e A156741 1;
%e A156741 1, 1;
%e A156741 1, 190, 1;
%e A156741 1, 7315, 7315, 1;
%e A156741 1, 134596, 5181946, 134596, 1;
%e A156741 1, 1562275, 1106715610, 1106715610, 1562275, 1;
%e A156741 1, 13123110, 107904771975, 1985447804340, 107904771975, 13123110, 1;
%t A156741 b[n_, k_]:= Binomial[2*n, 2*k];
%t A156741 T[n_, k_, m_]:= Round[Product[b[n+j, k+j]/b[n-k+j, j], {j,0,m}]];
%t A156741 Table[T[n, k, 8], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 19 2021 *)
%o A156741 (Magma)
%o A156741 A156741:= func< n,k | Round( (&*[Binomial(2*(n+j), 2*(k+j))/Binomial(2*(n-k+j), 2*j): j in [0..8]]) ) >;
%o A156741 [A156741(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 19 2021
%o A156741 (Sage)
%o A156741 def A156741(n, k): return round( product( binomial(2*(n+j), 2*(k+j))/binomial(2*(n-k+j), 2*j) for j in (0..8)) )
%o A156741 flatten([[A156741(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 19 2021
%Y A156741 Cf. A086645 (m=0), A156739 (m=6), A156740 (m=7), this sequence (m=8), A156742 (m=9).
%Y A156741 Cf. A151709 (row sums).
%K A156741 nonn,tabl
%O A156741 0,5
%A A156741 _Roger L. Bagula_, Feb 14 2009
%E A156741 Definition corrected to give integral terms and edited by _G. C. Greubel_, Jun 19 2021