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 A362588 #9 May 05 2023 07:44:34 %S A362588 1,1,0,1,2,0,1,6,12,0,1,12,72,144,0,1,20,240,1440,2880,0,1,30,600, %T A362588 7200,43200,86400,0,1,42,1260,25200,302400,1814400,3628800,0,1,56, %U A362588 2352,70560,1411200,16934400,101606400,203212800,0 %N A362588 Triangle read by rows, T(n, k) = RisingFactorial(n - k, k) * FallingFactorial(n, k). %F A362588 T(n, k) = (-1)^k * Pochhammer(n - k, k) * Pochhammer(-n, k). %F A362588 T(n, k) = binomial(n, k) * binomial(n - 1, k) * (k!)^2. %e A362588 Table T(n, k) begins: %e A362588 [0] 1; %e A362588 [1] 1, 0; %e A362588 [2] 1, 2, 0; %e A362588 [3] 1, 6, 12, 0; %e A362588 [4] 1, 12, 72, 144, 0; %e A362588 [5] 1, 20, 240, 1440, 2880, 0; %e A362588 [6] 1, 30, 600, 7200, 43200, 86400, 0; %e A362588 [7] 1, 42, 1260, 25200, 302400, 1814400, 3628800, 0; %e A362588 [8] 1, 56, 2352, 70560, 1411200, 16934400, 101606400, 203212800, 0; %p A362588 T := (n, k) -> (-1)^k*pochhammer(n - k, k)*pochhammer(-n, k): %p A362588 for n from 0 to 6 do seq(T(n, k), k=0..n) od; %Y A362588 Cf. A228229 (row sums), A002378 (column 1), A010790 (subdiagonal). %K A362588 nonn,tabl %O A362588 0,5 %A A362588 _Peter Luschny_, May 05 2023