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 A362847 #13 Oct 09 2023 14:30:10
%S A362847 1,1,3,1,15,105,1,35,945,10395,1,63,3465,135135,2027025,1,99,9009,
%T A362847 675675,34459425,654729075,1,143,19305,2297295,218243025,13749310575,
%U A362847 316234143225,1,195,36465,6235515,916620705,105411381075,7905853580625,213458046676875
%N A362847 Triangle read by rows, T(n, k) = 4^k * Gamma(n + k + 1/2) / Gamma(n - k + 1/2).
%F A362847 T(n ,k ) = (2*(n + k) - 1)!!/(2*(n - k) - 1)!!; 0 <= n <= k. - _Detlef Meya_, Oct 09 2023
%e A362847 [0] 1;
%e A362847 [1] 1, 3;
%e A362847 [2] 1, 15, 105;
%e A362847 [3] 1, 35, 945, 10395;
%e A362847 [4] 1, 63, 3465, 135135, 2027025;
%e A362847 [5] 1, 99, 9009, 675675, 34459425, 654729075;
%e A362847 [6] 1, 143, 19305, 2297295, 218243025, 13749310575, 316234143225;
%p A362847 T := (n, k) -> 4^k * GAMMA(n + k + 1/2) / GAMMA(n - k + 1/2):
%p A362847 seq(seq(T(n, k), k = 0..n), n = 0..7);
%t A362847 T[n_,k_]:=(2*(n+k)-1)!!/(2*(n-k)-1)!!;Flatten[Table[T[n,k],{n,0,7},{k,0,n}]] (* _Detlef Meya_, Oct 09 2023 *)
%Y A362847 Cf. A362848 (row sums), A000466 (column 1), A101485 (main diagonal).
%K A362847 nonn,tabl
%O A362847 0,3
%A A362847 _Peter Luschny_, May 05 2023