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