%I #14 Sep 08 2022 08:46:10

%S 1,1,1,2,4,2,6,18,18,6,6,24,36,24,6,30,150,300,300,150,30,20,120,300,

%T 400,300,120,20,140,980,2940,4900,4900,2940,980,140,70,560,1960,3920,

%U 4900,3920,1960,560,70,630,5670,22680,52920,79380,79380,52920,22680,5670,630

%N Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.

%F T(n,k) = C(n,k)*A056040(k).

%F T(2*n,n) = C(2*n,n)^2.

%e Triangle begins:

%e . 1;

%e . 1, 1;

%e . 2, 4, 2;

%e . 6, 18, 18, 6;

%e . 6, 24, 36, 24, 6;

%e . 30, 150, 300, 300, 150, 30;

%e . 20, 120, 300, 400, 300, 120, 20;

%e . 140, 980, 2940, 4900, 4900, 2940, 980, 140;

%e . 70, 560, 1960, 3920, 4900, 3920, 1960, 560, 70;

%e . 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630; etc.

%p T := (n,k) -> n!*binomial(n,k)/(iquo(n,2)!)^2:

%p seq(print(seq(T(n,k), k=0..n)), n=0..9);

%o (Magma) [Binomial(n,k)*Factorial(n)/Factorial(Floor(n/2))^2: k in [0..n], n in [0..10]]; // _Bruno Berselli_, Feb 02 2015

%Y Cf. A021012, A196347, A002894.

%Y Row sums are A253665.

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, Feb 01 2015