A362588 - OEIS

%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