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 A171822 #6 Feb 23 2021 08:31:22
%S A171822 1,1,1,1,9,1,1,30,30,1,1,70,225,70,1,1,135,980,980,135,1,1,231,3150,
%T A171822 7056,3150,231,1,1,364,8316,34650,34650,8316,364,1,1,540,19110,132132,
%U A171822 245025,132132,19110,540,1,1,765,39600,420420,1288287,1288287,420420,39600,765,1
%N A171822 Triangle T(n,k) = binomial(2*n-k, k)*binomial(n+k, 2*k), read by rows.
%H A171822 G. C. Greubel, <a href="/A171822/b171822.txt">Rows n = 0..100 of the triangle, flattened</a>
%F A171822 T(n, k) = binomial(2*n-k, k)*binomial(n+k, 2*k) = A054142(n, k)*A085478(n, k).
%F A171822 Sum_{k=0..n} T(n, k) = Hypergeometric 4F3([-n, -n, 1/2 -n, n+1], [1/2, 1, -2*n], 1) = A183160(n). - _G. C. Greubel_, Feb 22 2021
%e A171822 Triangle begins as:
%e A171822 1;
%e A171822 1, 1;
%e A171822 1, 9, 1;
%e A171822 1, 30, 30, 1;
%e A171822 1, 70, 225, 70, 1;
%e A171822 1, 135, 980, 980, 135, 1;
%e A171822 1, 231, 3150, 7056, 3150, 231, 1;
%e A171822 1, 364, 8316, 34650, 34650, 8316, 364, 1;
%e A171822 1, 540, 19110, 132132, 245025, 132132, 19110, 540, 1;
%e A171822 1, 765, 39600, 420420, 1288287, 1288287, 420420, 39600, 765, 1;
%e A171822 1, 1045, 75735, 1166880, 5465460, 9018009, 5465460, 1166880, 75735, 1045, 1;
%t A171822 Table[Binomial[2*n-k, k]*Binomial[n+k, 2*k], {n,0,10}, {k,0,n}]//Flatten
%o A171822 (Sage) flatten([[binomial(2*n-k, k)*binomial(n+k, 2*k) for k in (0..n)] for n in (0..10)]) # _G. C. Greubel_, Feb 22 2021
%o A171822 (Magma) [Binomial(2*n-k, k)*Binomial(n+k, 2*k): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Feb 22 2021
%Y A171822 Cf. A054142, A085478, A183160.
%K A171822 nonn,tabl
%O A171822 0,5
%A A171822 _Roger L. Bagula_, Dec 19 2009
%E A171822 Edited by _G. C. Greubel_, Feb 22 2021