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A253666 Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.

%I A253666 #14 Sep 08 2022 08:46:10
%S A253666 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 A253666 400,300,120,20,140,980,2940,4900,4900,2940,980,140,70,560,1960,3920,
%U A253666 4900,3920,1960,560,70,630,5670,22680,52920,79380,79380,52920,22680,5670,630
%N A253666 Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.
%F A253666 T(n,k) = C(n,k)*A056040(k).
%F A253666 T(2*n,n) = C(2*n,n)^2.
%e A253666 Triangle begins:
%e A253666 .   1;
%e A253666 .   1,    1;
%e A253666 .   2,    4,     2;
%e A253666 .   6,   18,    18,     6;
%e A253666 .   6,   24,    36,    24,     6;
%e A253666 .  30,  150,   300,   300,   150,    30;
%e A253666 .  20,  120,   300,   400,   300,   120,    20;
%e A253666 . 140,  980,  2940,  4900,  4900,  2940,   980,   140;
%e A253666 .  70,  560,  1960,  3920,  4900,  3920,  1960,   560,   70;
%e A253666 . 630, 5670, 22680, 52920, 79380, 79380, 52920, 22680, 5670, 630; etc.
%p A253666 T := (n,k) -> n!*binomial(n,k)/(iquo(n,2)!)^2:
%p A253666 seq(print(seq(T(n,k), k=0..n)), n=0..9);
%o A253666 (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 A253666 Cf. A021012, A196347, A002894.
%Y A253666 Row sums are A253665.
%K A253666 nonn,tabl
%O A253666 0,4
%A A253666 _Peter Luschny_, Feb 01 2015