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 A356636 #6 Aug 19 2022 02:48:25
%S A356636 1,1,1,4,8,4,36,108,108,36,144,576,864,576,144,3600,18000,36000,36000,
%T A356636 18000,3600,14400,86400,216000,288000,216000,86400,14400,705600,
%U A356636 4939200,14817600,24696000,24696000,14817600,4939200,705600
%N A356636 Triangle read by rows. T(n, k) = binomial(n, k) * n!^2 / floor(n/2)!^2.
%F A356636 T(n, 0) = T(n, n) = A193282(n).
%F A356636 Sum_{k=0..n} T(n, k) = 2^n * A193282(n).
%e A356636 Triangle T(n, k) starts:
%e A356636 [0] 1;
%e A356636 [1] 1, 1;
%e A356636 [2] 4, 8, 4;
%e A356636 [3] 36, 108, 108, 36;
%e A356636 [4] 144, 576, 864, 576, 144;
%e A356636 [5] 3600, 18000, 36000, 36000, 18000, 3600;
%e A356636 [6] 14400, 86400, 216000, 288000, 216000, 86400, 14400;
%p A356636 A356636 := (n, k) -> binomial(n, k) * (n! / iquo(n, 2)!) ^ 2:
%p A356636 for n from 0 to 9 do seq(A356636(n, k), k = 0..n) od;
%Y A356636 Cf. A056040, A193282, A253666.
%K A356636 nonn,tabl
%O A356636 0,4
%A A356636 _Peter Luschny_, Aug 19 2022